The short answer is that the Third Reich was basically a bunch of competing factions wherein leadership was centered around powerful, charismatic leaders, all of whom competed for the patronage of Adolf Hitler. This is called Führerprinzip, or leader principle, and was the basis for all political thought within the Third Reich. At no time during Adolf Hitler's rise to power, leadership in peacetime, leadership in wartime, and capitulation of the Reich in 1945 did factions within Hitler's government not exist. Though they tried to portray the Reich as a well oiled machine efficiently leading the German people to an inevitable victory, the truth is that the Reich was dysfunctional and chaotic at times, with different government factions only able to carry out its duties based on how much favor it could curry with Der Fuerher.

Nazism as we know it developed within the Deutsche Arbeiterpartei or German Worker's Party as founded by Anton Drexler, Dietrich Eckart, Gottfried Feder, Karl Harrer in the Weimar Republic on 5 January 1919. Drexler was the real idealogue of the party and contributed both hard nationalism / pan-Germanism and hardline antisemitism. Eckart was a prolific writer, journalist, poet, and playright who took these same ideas and encapsulated them in as many forms of media as possible, it seems. Feder was an economist and is the founder of third position economics, both anti-capitalist and anti-communist; he rejected Marx's notion that socialism was an interim stage leading from crumbling capitalism to communism and instead posited that socialism could be made to work for the interests of a national people. Hence, national socialism. Harrer was perhaps the most different out of the four and was opposed personally to both Hitler and mobilization of the Party as a mass movement; for Harrer, the Party was always to be an elite and semi-secret society.

Both Drexler and Harrer were members of the Thule Society, a secret society made up of disaffected Great War veterans in Germany. The Thule Society is responsible for what you call the Blood and Soil faction, but more properly Völkische Bewegung, the "folkish movement". The entire idea of Blut und Ehr is Volkskörper, or the idea that a people and the land they toil on are inseparable. They were also already using the swastika -- not yet the Hakenkreuz -- but more importantly they originated the overarching "Aryan Race" mythology that so permeated everything about the NSDAP. Their constructed mythology drew on Indo-European mythology, Greco-Roman religion, and German paganism to create the idea of a master race.

These four men and this society were by no means a minority. It must be very well understood that these were popular ideas embraced by the German people in the wake of the November Revolution of 1918-1919: on 9 November 1918, Kaiser Wilhelm II voluntarily abdicated the throne. A National Assembly was called and millions of German workers went on strike in an attempt to establish socialism in Germany in the wake of the Bolshevik uprising in 1917 that Germany herself had helped along! The German people more than anything desired peace; this led directly to the Sailor's Revolt of 24 October 1918 and Germany embraced revolution. A brief but bloody civil war gave birth to the stab-in-the-back legend: an attempted socialist uprising calling itself the "Free Socialist Republic of Germany" established council democracy and arrested anyone associated with the Emperor or the Imperial regime. The Freikorps here emerge as another faction: these were Imperial German soldiers who were genuinely angry at peace and believed they could have won the war. When all hell broke loose on their own soil, they easily embraced the conflict. By 11 August 1919, the new constitution of the Weimar Republic had been written but the Freikorps were still gunning for blood.

Your "Willhelmine faction" and the "Hindenburgers" are found here as well. Willhelminism is best understood literally by looking at Kaiser Wilhelm II himself. Under his rule the Second Reich (the Holy Roman Empire being the First Reich in period German popular thought) was grandiose, imperial, monarchist, and conservative. "Hindenburgers" were not terribly different; they only exchanged the dressings of empire for republic and owed strong allegiance to Paul von Hindenburg, the commander of Germany's army during the Great War. So these two that you may have heard in passing are really best understood as groups of battle-hardened German soldiers strongly latching on to all things quintessentially German.

Adolf Hitler in 1919 could easily be called one or either of these things. Ironically, Hitler's first official run in with the DAP was acting in his capacity as a Reichswehr soldier on the direct orders of his superior officer, Captain Karl Mayr. He was to infiltrate and influence the German Worker's Party. Of course, the Party members took strong note both of Hitler's sympathy for their own views as well as his strong oratory skills and direct, militant manner.

1920 was the year that Hitler used his skills to take the party public, which both alienated Harrer and caused him to resign. This is the beginning in a long trend for the rest of Hitler's life: destroying factions which are opposed to his goals in the long run. Hitler and the other founding members of the Party clarified the Party's position in "Twenty Five Points", an easily digestible manifesto for the masses. No longer was this ideology the reserve of the intelligentsia, but for the masses. On 24 February 1920, the DAP officially became Nationalsozialistische Deutsche Arbeiterpartei. Hitler personally objected to the use of the word "socialist" within the Party's name, but upon explaination that this was to appeal to left-wing workers as well as the hard right wing and conservative / monarchist elements, he accepted.

By 1921, Hitler had replaced Drexler as Party chair and reorganised Party member's Emil Maurice's "hall protection squad" as the Sturmabteilung or Storm Division. The Stormtroopers or SA were the precursor to the SS. The paramilitary ultimately came under the leadership of Ernst Röhm who had joined the DAP at roughly the same time Hitler did; Röhm himself would be executed during Kristallnacht and the SA liquidated and repurposed as the SS. In 1922, Hitler and the Party formed the Hitler Youth, which would infamously go on to become one of the most die-hard Nazi factions. That same year on 31 October, Mussolini's fascist blackshirts seized power in Italy. There was no "fascist faction" within the NSDAP; Hitler and the Party embraced them and borrowed much of their style.

Devotion towards Hitler and expression of the Führerprinzip only intensified until in 1925 the NSDAP attempted the Beer Hall Putsch, leading to the death of fourteen party members. This event in and of itself was schismatic within the nascent NSDAP: everyone had to ask themselves whether they were willing to die for this cause and the Fuerher or not. Hitler's jailing and the NSDAP's ban on 9 November 1923 was even further schismatic: The National Socialist Freedom Movement was founded in 1925 as a direct competitor to the NSDAP. It was formed by the hard-right Volkish elements within the Party that thought Hitler's time had come and gone. The NSDAP survived during Hitler's incarceration largely due to the influence of Joseph Goebbels, who in and of himself represented a faction of sorts. Hitler is released 20 December 1924, the NSDAP is relegalized in 1925, and Hitler forms his own personal bodyguard and calls it the Schutzstaffel or ϟϟ.

Until the legal establishment of the Third Reich in 1933 all of these elements would continue to compete with one another for Hitler's favor as his sway over the German public grew larger and larger.

---

BIBLIOGRAPHY

Der Fuehrer: Hitler's Rise to Power, Konrad Heiden 1944

The Rise and Fall of the Third Reich, William L. Shirer 1960

The Mind of Adolf Hitler, Walter C. Langer 1944 (1972?)

The Einsatzgruppen Reports, Arad, Yitzhak, et al., eds. Selections from the Dispatches of the Nazi Death Squads’ Campaign against the Jews in Occupied Territories of the Soviet Union, July 1941–January 1943. New York: Holocaust Library, 1989.

Cecil, Robert. The Myth of the Master Race: Alfred Rosenberg and Nazi Ideology. New York: Dodd Mead & Company, 1972.

Bramsted, Ernest K. Goebbels and National Socialist Propaganda, 1925-1945. East Lansing, MI: Michigan State Press, 1965.

Overy, Richard J. Goering: The 'Iron Man'. London: Routledge Kegan Paul, 1984.

Manvell, Roger, and Heinrich Fraenkel. Heinrich Himmler: The Sinister Life of the Head of the SS and Gestapo. New York: Skyhorse Publishing, 2007.

Goodrick-Clarke, Nicholas (1985). The Occult Roots of Nazism: The Ariosophists of Austria and Germany 1890-1935. Wellingborough, England: The Aquarian Press.

Mark Jones: Founding Weimar. Violence and the German Revolution of 1918–19, Cambridge University Press, Cambridge 2016

If you're as interested in learning about these depraved bastards as I am, here's an overwhelming bibliography