The events in Chemnitz, analysts say, showcase the symbiotic relationship between the neo-Nazis and the Alternative for Germany, which officially distances itself from such groups.

The party has done a lot to normalize the language of the far right. If the slogans heard on the streets of Chemnitz this week — from “lying press” to “Germany for the Germans” — have lost their shock value, it is because variations of them are now regularly heard in Parliament.

“We have a strong neo-Nazi scene in eastern Germany, but we also have a strong current of far-right extremism in all of Germany — not just in Parliament but in society,” said Matthias Quent, who runs an institute that studies democracy and civil society in the eastern state of Thuringia.

That is why the far right is so self-confident, he said: “They think their day has come.”

Social media played a significant role in mobilizing the mobs.

Within hours of the stabbing last Sunday, soccer hooligans with links to the neo-Nazis posted an appeal online: “Let’s show together who has the say in this city.”

Soon rumors started circulating. The victim had been defending a woman who had been molested by the killer. A second victim had died in hospital. Neither was true. But within a few hours, some 800 protesters were on the streets, outnumbering the police 10 to one.

The AfD was quick to chime in. “When the state can’t protect its citizens anymore, the citizens take to the street and protect themselves,” Markus Frohnmaier, a lawmaker for the party, said in a Twitter post. “Today it is a citizen’s duty to stop the deadly ‘knife migration!’ ”