Glad you asked, Eugine:

The party denies that it has any official connection to Neo-Nazism. Although it uses the Roman salute, a salute used by the Italian Fascist and German National Socialist movements, it claims to draw its inspiration in this primarily from the 4th of August Regime established by Ioannis Metaxas...Likewise, the Golden Dawn's meander symbol, while sometimes compared to the National Socialist Swastika, is according to Golden Dawn a symbol drawn from Greek art, which the party sees as representing bravery and eternal struggle.[18][128]

Ilias Kasidiaris, a spokesman for Golden Dawn, wrote an article that was published in Golden Dawn magazine on 20 April 2011, in which he said, "What would the future of Europe and the whole modern world be like if World War II hadn't stopped the renewing route of National Socialism? Certainly, fundamental values which mainly derive from ancient Greek culture, would be dominant in every state and would define the fate of peoples. Romanticism as a spiritual movement and classicism would prevail against the decadent subculture that corroded the white man. Extreme materialism would have been discarded, giving its place to spiritual exaltation". In the same article, Adolf Hitler is characterized as a "great social reformer" and "military genius".[129]

In an article published in 1987 in the Golden Dawn magazine titled "Hitler for 1000 years", its editor Michaloliakos [see below] showed his support for Nazism and white supremacy.[130] Specifically he wrote, "We are the faithful soldiers of the National Socialist idea and nothing else" and "[...] WE EXIST, and continue the battle, the battle for the final victory of our race".[130] He ends the article by writing "1987, 42 years later, with our thought and soul given to the last great battle, with our thought and soul given to the black and red banners, with our thought and soul given to the memory of our great Leader, we raise our right hand up, we salute the Sun and with the courage, that is compelled by our military honor and our National Socialist duty we shout full of passion, faith to the future and our visions: HEIL HITLER!".[130]

...The founder of the party, Nikolaos Michaloliakos, appeared to give a Nazi salute in the Athens city council. He claims that it was merely "the salute of the national youth organisation of Ioannis Metaxas".[128][136]

Of course, society normally finds it easy to recognize and ostracize such blatantly dishonest Nazism. It doesn't create any actual confusion - unless people have gone out of their way to weaken society's immune system, eg by deliberately signalling Nazism when the reality is more obscure.