Arendt wrote a bit about this in Eichmann in Jerusalem and The Origins of Totalitarianism. I won't pretend to have a full understanding of her case, but she claimed that the Nazis maintained a crucial distinction between the "movement" and the state, with the former retaining primacy and never being fully absorbed by the latter, with the result that "All real power is vested in the institutions of the movement, and outside the state and military apparatuses. It is inside the movement, which remains the center of action of the country, that all decisions are made; the official civil services are often not even informed of what is going on..." In this division, the secret police rather than the military serves as the movement's instrument of coercion. She also stresses the warped nature of the understanding of "legality" in totalitarian states, with notions of "right" and "wrong" completely subordinated to the will of the leader, the only reliable measure of lawfulness. Thus Eichmann could legitimately claim to have broken no laws in executing orders, or in the case when he defied written orders received from Himmler by arguing they defied the higher, unwritten will of Hitler.
I'm aware there is a lot of controversy and pushback concerning her arguments but I can't say much about it.