I read a biography on Reinhard Heydrich and I was surprised by the sheer amount of competing factions in the Nazi government. However since the biography did focus on Heydrich, the book only mentioned political factions when it concerned Heydrich's power. How many factions were there, how influential were these factions, and did this factional infighting affect the out come of the war.
An interesting source here is Albert Speer's Infiltration; Speer was Hitler's Minister of Armaments after 1942, and the book is largely about the way Himmler's SS and the Ministry of Armaments kept butting heads. To hear Speer tell it, Himmler's efforts to build a postwar power base--the SS has been well described as a state within a state--kept sabotaging Speer's efforts to run a war.
I don't actually recommend reading Infiltration, but here are some examples from it:
Himmler kept having the Gestapo (which he controlled) arrest prisoners on trumped-up charges; these prisoners were working in Speer's factories but would then wind up in SS-run factories. So the arrests were a way of poaching labor away from Speer.
That was part of a larger power struggle over what to do with prisoners, Jews, and so on; Speer makes it clear that he never saw them as anything except a resource to be used ("Today, almost forty years later, I grow dizzy when I recall that the number of manufactured tanks seems to have been more important to me than the vanished victims.") But that makes him seem like an absolute saint in contrast with Himmler (and Goebbels's) plans involving extermination and enslavement for its own sake. He makes a good case that the production in SS factories and places like Auschwitz was pathetically low, so every time Himmler got prisoners that could have gone to Speer the war effort suffered.
Both Speer's ministry subordinates and the industrialists who actually ran the factories kept running afoul of the SS; although Speer was mostly able to protect his people, the impression he gives is that if he had fallen from power, Himmler was ready to arrest his top people and take over. It's not clear how much that climate of fear interfered with productive efficiency, but it can't have helped.
Speer was (to hear Speer tell it) not a fan of crank plans like making rubber out of dandelions or oil out of trees, while the promoters of these plans had a ready ear in Himmler; precious resources were wasted on these ideas.
Interestingly, according to Speer this infighting never stopped--there was never a point at which anyone said, hey, the Russians are next door and we need to get serious:
Everywhere, the battle for jurisdictions was being fought even in the final weeks, between ministries and in the intermediate agencies, as though the Reich were invincible.
It seems that the general perception of the Nazi state is often a belief that it was a highly organised, and effective dictatorship. To be frank, it couldn't have been further from the truth. The Nazi "government" was ultimately a systemless non-state, operating in neo-feudalist chaos.
The medieval feudal system was born out of a religious belief that posited a divine hierarchy of rule, stemming from God down to Kings, allowing them the divine right to rule and distribute power amongst their followers as they saw fit. The Nazi state operated on a similar principle but you replace the role of God with Hitler. The myth of the Fuhrer is well documented, his personal authority was unquestioned, and his word was literally law. The problem is, he was never really keen on actually ruling, and tended to seize on something, and then lose interest. This tendency manifested itself in the way that he would appoint people to ministerial posts, and then later create entire departments, or new posts that directly impinged upon the positions of others.
The lack of any form of system to the Nazi regime makes any clear understanding almost impossible: indeed, the Hitler regime itself was 'inimical to a rational order of government and administration.' Through a highly personalised system of charismatic rule 'the overall structure of government was reduced to a shambles of constantly shifting power-bases and warring factions'. Hitler's own personal authority functioned as an 'enabler', and his preference for what was usually the most radical course of action, or in favouring his closest friends over others meant that the existing structures of the state were often destroyed and replaced by individuals battling amongst each other for Hitler's favour through the use of radical policies and their own influence with the Fuhrer. This resulted in a vast array of different factions, all struggling for power. The factions themselves were prone to fragmenting within themselves into sub-factions, seriously harming the war-effort.
Sources to look at (two are articles): Ian Kershaw, 'Working Towards the Fuhrer': Reflections on the nature of the Hitler dictatorship, The Journal of European History Vol. 2 Hans Mommsen, Cumulative radicalisation and progressive self-destruction as Structural Determinants of the Nazi dictatorship in Stalinism and Nazism Dictatorships in comparison Karl Dietrich Bracher, The German Dictatorship: the origins, structure and consequences of National Socialism