I am not sure if there were other organized parallel resistance cells within the German military during wartime, but at least for the most famous and successful one - which I will call the Stauffenberg-Tresckow group (the ones behind Operation Valkrie/July 20, and apart of the Schwarze Kappelle officer group) - it is known that the officers comprising the group were mostly conservative nationalist types who had initially supported Hitler and Nazism before turning against Hitler. As such, the reason why they went against Hitler was because they saw that he was leading them into destruction and a total reversal of all gains they had made, as well as many being against the genocide that was being carried out against Jews. But just because many (or all) were opposed to the systematic mass-killings of Jews didn't mean that they were against all Nazi racial policies. In fact, some of them wished to continue many of its racial policies if possible and were known self-confessed supporters of its racial objectives (including Stauffenberg himself). They also didn't really wish to give up all the land Germany had occupied during wartime, and agreed on demanding the allies to let them annex portions of Poland, if not all of it, into post-wartime/coup Germany, as well as all of Sudetenland and Austria. Hence, its clear that the main motive behind anti-Hitler motives amongst the resistance officers were driven by the wish to secure what Germany still had at the time and avert calamitous military disaster, foreign occupation and invasion, and a loss of their gains. As for assassinating Hitler, not all officers initially gave support for an assassination as they were mostly divided into two opinions on whether to assassinate him or to make him stand trail, but all agreed on his DEPOSITION, although there was a marked shift to the former opinion after the staggering casualty figures started coming in from the eastern front and the need for an immediate removal of power became apparent. This apparent urge to act culminated in the failed July 20 plot where they hoped and agreed to the need on assassinating the Fuhur (and Himmler). After the assassination, they hoped to smoothly trigger their takeover coup as per implementation of Operation Valkyrie wherein command of the Wehrmacht and executive powers were transferred to a senior military member of the Tresckow-Stauffenberg group, with the SS merging into the Wehrmacht (a still-independent SS was a potential obstacle to their coup, so their merging with the Wehrmacht would put them directly under the control of the resistance). The officers also planned to have the secretly-allied German military commander of France (a senior member of the Schwarze Kapelle officer group, the military resistance group the Tresckow-Stauffenberg stems from) immediately negotiate an armistice with the allies, ending the war. They had already planned and set aside all key German government offices for resistance members from both military and civilian circles, with a larger share going towards officers within the Tresckow-Stauffenberg/Schwarze Kapelle group. This planned government would be a continuity of the former Nazi one, keeping intact all state institutions for the most part whilst removing all Nazi elements, and will retain control over most - if not all - of the occupied German-inhabited territories of Austria, Sudetenland, and maybe Alsace and Lorraine.

Their plan was bound to fail. From a military point of view, Germany had lost the war already by July 1944. The Allies would have insisted on unconditional surrender, and the military leaders would have had to accept their terms. That would have given Germany a new "Dagger in the Back" legend: Hitler would have saved Germany from defeat, had his generals not assassinated him.

The Stauffenberg-Tresckow group had extensive talks through secret diplomatic channels with the Allies. They had insisted on the abandonment of the policy of unconditional surrender and wanted some political and territorial guarantees for a post-Hitler Germany if they were to make peace with the allies when they were in power. Yet the allies would not budge with the demand for Unconditional Surrender for Germany. So in the end the Stauffenberg-Tresckow group figured that eventhough there was an unlikeliness that they would be able to keep some of their gains in the east, and that they would not rule Germany as a military-authoritarian state. The group still felt like they were obligated to do carry on with the plot because as general beck said "it could bring the war to an end and save further loss of blood and destruction of the Fatherland' and that "perhaps at least the Western Allies, despite their terms of unconditional surrender, might not be too hard on a conquered Germany."

Why they resisted? Although there were many forms of resistance to Hitler from different groups, I'll focus on some of the leaders of the July 20th plot.

For some of the civil servants such as former mayor of Leipzig, Carl Goerdeler, he had hoped they would share power with the Nazis and initially supported them during their rise to power. Once Nazi party officials began to infringe on the authority of the civil service and it became clear that a permanent sharing of power between the party and bureaucracy would never take place, Goerdeler resigned as mayor. To Goerdeler, the Nazi movement had failed to live up to its ideals and made the common mistake of dictators by snatching at power and abusing it. The fatal flaw in the National Socialist movement was in its policies and judgments not in its ideals. Although he still agreed with some policies of the regime, and admitted that Germany’s eastern boundary should be moved at Poland’s expense he began to oppose the regime.

Once Hitler moved to put an end to the relative autonomy of the diplomatic corps in 1938 by appointing Joachim von Ribbentropp as minister of foreign affairs, did many members of the civil service begin to see the writing on the wall and begin to oppose the regime. Members of the bureaucratic resistance didn’t turn against the regime for any one reason. Some opposed Nazi policy toward the Jews and deplored the Nuremberg Laws and Kristallnacht. Some such as Urlich von Hassell opposed the nazification of the civil service. In many cases it was possible to still support the regime in some areas and oppose it in others. It was only during the war and its lead up when they finally saw Hitler for what he was and saw the looming disaster, and heard hints of the exterminations of scores of people did the remaining doubts disappear.

In the wake of the Fritsch affair the first stirrings of military resistance began to grow. Groups centered around older generals such as Ludwig Beck, and Hans Oster—chief of military intelligence—began to materialize in a variety of locations. They recognized the threat that Hitler posed to their position and Germany. The “disgraceful farce” leading to the dismissal of Fritsch gave Oster the determination to resist. What the Fritsch affair signaled was Hitler’s attempts to start replacing the military leadership with his own men. Beck did not become an opponent of the regime until 1938. Although he occasionally made critical remarks, he differentiated between the “well intentioned Hitler” and the Nazi party radicals.

The crisis in the summer of 1938 over the Sudeten region turned the growing disgruntlement in the military into outright sedition. Small groups in the civil service and armed forces began to meet informally criticize the regime, and make plans to prevent a war that would surely devastate their country. When plans for the invasion of Czechoslovakia began to take shape that summer, Beck was spurred into action. At first he considered a mass resignation of the general staff, but later he was the only one to resign, effectively removing himself from a position of power in the military. Although he still received widespread support among the officers, he was now powerless. His successor, Franz Halder, shared Beck’s sentiments that invading Czechoslovakia would lead to a wider European war that would be a disaster for Germany. Plans for a coup began to take shape between Oster, Halder, Beck, Goerdeler, and other military officers and members of the civil servant resistance. Once Halder issued the signal, a party would raid the Reich Chancellery and arrest Hitler. Their plans were derailed by the Munich conference. A similar plot was planned prior to the invasion of Poland and the Western European countries, but this also was dashed.

From autumn 1941 onward, a new opposition developed under the younger staff officers. Henning von Tresckow, Senior Operations Officer in Army Group Center was the driving force behind this new group. He dispatched Fabian von Schlabrendorff to Berlin to make contact with the civilian opposition around Beck. He placed men that sympathized with his line of thinking in commands within his army group and laid the foundations for a resistance group. Tresckow attempted to arrange for the arrest of Hitler in the eastern military headquarters in Russia, when that failed he began to plan for a coup. A scenario—codenamed Valkyrie—was developed to prevent an uprising of slave workers in Berlin. In actuality, this was a cover for the military to seize key buildings in the event of Hitler’s arrest or assassination. He entrusted the execution of the coup to Count Claus Schenk von Stauffenberg. It was under Tresckow, that the military became the driving force of the conspiracy. For Stauffenberg and Tresckow military considerations weighed most heavily. Maintaining the army intact and preventing a devastating military defeat were their prime considerations.

Although the motives of the military resistance were varied, one of the most important was their concern for the units under their command and to keep the army intact. There was also criticism of the way Hitler had handled the war, by interfering with operational decisions, which showed his contempt for professional officers.

The resisters felt that the regime had exceeded the bounds of a firm but just exercise of authority and had become despotic and corrupt.

Post coup plans? The July 20th plotters had hoped to make peace with the allies by getting them to abandon their policy of unconditional surrender and being allowed to keep any territorial gains. They then would be allowed to turn their full attention on the Soviet Union either by themselves or with western support. There was also talk of a proposed allied landing at Hamburg.

In the aftermath of the assassination, there had also been preliminary plans to appoint Ludwig von Beck as head of any future provisional government with Ulrich von Hassell as head of the foreign office and Erwin Rommell playing a prominent role

Sources:

Fest, Joachim. Plotting Hitler’s Death: The Story of the German Resistance

Hamerow, Theodore, S. On the Road to the Wolf’s Lair: The German Resistance to Hitler.

Hoffmann, Peter. The History of the German Resistance 1933-1945

Hassell, Ulrich von. The Von Hassell Diaries: 1938-1944.

Mommsen, Hans. Alternatives to Hitler: German Resistance Under the Third Reich.