Correct, and that was my point and the reason I used "National Socialist" instead of the more well known "NAZI" description, to get the correct word "socialist" in.
As a point of fact, the NAZIs were actually national communists, as opposed to the Russians who were international communists. Hitler was a communist who refused to take orders from Moscow, so he set up his own communist party in Germany, the NAZI party, pretty much as far left as you can get.
Their nationalism was IMHO grand-tactical. They had to attract the support of the very nationalist army officer corps, for one thing, and for another, by 1920, Germany had pickled intellectually for about 50 years in "Pan-Germanism", which was ethnocentric and intensely antisemitic and anti-Slavic.