Exactly - including the communists and the Social Democratic Party of Germany, a.k.a. the actual socialists.
I have no idea where this "Fascism is actually left-wing" bullshit first popped up, but it's wrong and dangerously so. There's a certain brand of conservative that is vehemently in denial that their political ideology could ever be associated with evil, which is both staggeringly revisionist and wilfully blind. People should be willing to face the ugliness on the fringes of their movements and that appears to be something that only right-wingers (or, more specifically, a subset of right-wingers) lack the fortitude to do - I've never seen a leftist try to claim that "Communism is actually a right-wing form of government" or some other such nonsense, and the communist dictatorships of the mid-20th century have just as much blood on their hands as the far-right fascist governments of the early century.
And it's not like this is hard to figure out. Nazism was born out of the Freikorps, groups of paramilitary vigilantes that emerged from World War I as one of the strongest right-wing anti-communist forces in the country, who thought little of butchering accused leftists wherever they found them. Prior to the start of World War II, Hitler was a darling of the American right, who saw him as one of the most effective fighters against the spread of communism in all of Europe (and given that antisemitism was not uncommon in right-wing politics of the day, Hitler's anti-Jewish policies were, if not publicly lauded, at least privately admired) - Henry Ford even wrote a creepy ode to Hitler in the German version of his private right-wing, virulently antisemitic newspaper, the Dearborn Independent (and the feeling was mutual - Hitler gave a shout-out to Ford in Mein Kampf and called him an inspiration).
Seriously, learn your history before you spout off this sort of nonsense.
First of all, that is that those two paragraphs saying basically "Nope. It is right wing because it is right wing, and several influential individuals who hated communism loved Hitler".
There is a reason why the Molotov-Ribbontrop pact was signed, and one week later, Germany invaded Poland. The Soviet Union declined to intervene, but eventually caused a war shortly afterwards when the Soviet Union was invaded in 1941, and started the fighting between the two countries in World War 2. Between 1939 and 1941, there was propaganda between the two countries praising them.
The pact was signed, because the two ideologies are similar. But in truth, it was basically a short-term peace treaty between two genocidal dictators which cost 72 million lives from across all continents except Antarctica in order to preserve freedom from one of these monsters, and for punishment for genocide. Germany decided to invade the Soviet Union first.