Were the Nazis socialist?

On Denis de Rougemont, a literary and cultural Swiss philosopher:

"After a few weeks in Frankfurt, he found himself wondering, 'le régime est-il de gauche ou de droite? [Is the regime on the left or the right?]’ What unsettled him was the fact that those who stood most naturally on the right - lawyers, doctors, industrialists and so on — were the very ones who most bitterly denounced National Socialism. Far from being a bulwark against communism, they complained, it was itself communism in disguise. They pointed out that only workers and peasants benefited from Nazi reforms, while their own values were being systematically destroyed by devious methods. They were taxed disproportionately, their family life had been irreparably harmed...

In a letter to her sister Debo several years later, Nancy Mitford wrote, 'Actually I have always said that there wasn't a pin to put between Bolshies & Nazis except that the latter, being better organised, are probably more dangerous.'"

--- Travellers in the Third Reich: The Rise of Fascism Through the Eyes of Everyday People / Julia Boyd