No, Nazism is another sort of socialism. Technically, the correct word here probably is “corporatist”, which does not mean what it sounds like.
Its a “third way” system, out of the many that were popular in the 1890’s-1930’s. You have a vast variety of these ideas, from the “Rerum Novarum” of Leo XIII to the Portuguese, Italian, Spanish, etc. variants of “third ways”.
Its got its own peculiarities, in that it is fundamentally antisemitic. No antisemitism = no Nazism.
As for its marxist links, it draws more from Leninism, as to the primacy of the “vanguard”, the party. Marx did not describe an operable form of communism.
And none of these things have anything to do with the modern degenerate forms of Marxism (which itself is probably best thought of a degenerate Christian heresy), which are prevalent today. We are talking of the legacy of Marcuse, etc., where the working class no longer matters. They betrayed the intellectuals you know.
Hitler admitted that he had adopted some ofarxism.