It makes sense, but it would be a mistake to confuse Nazism with socialism. It was a weird hodge-podge of nationalistic, racial and philosophical tenets that appealed to the uneducated and those wishing to control the uneducated while fighting the threat of communism (the cure was just as bad as the disease). Goodle "Nazi philosophy" or "National Socialism Nazis" and look at the dictionary definitions that come up and you'll see a weird stew of ideas and concepts, including fascist doctrine.
When I think of Nazis and Communists, it's like that Monty Python bit in "Life of Brian" about the People's Front of Judea and the Judean People's Front. Essentially they were the same thing, but reserved the most hatred for each other. "Splitters!"