AfD just won 44% in a German state. Now Germany's firewall faces its biggest test.

Germany's far-right Alternative for Germany (AfD) won a record 44% in Saxony-Anhalt on Sunday, leaving a small party with seats that could determine whether it can lead the nation's first far-right state government since World War II.

Why it matters: Germany rebuilt its democracy after Nazi rule with unusually strong safeguards against extremism.

AfD's breakthrough shows those barriers aren't stopping Europe's far right from becoming dominant electoral forces.

The latest: AfD more than doubled its 20.8% share in 2021, hitting its highest vote share ever in a state election and finishing ahead of the center-right CDU at 17%.

BSW, the party that hasn't ruled out working with the AfD, barely cleared the 5% threshold parties need for parliamentary representation.

Together, AfD and BSW would hold 43 seats, one more than a majority.

BSW, a populist party, combines far-left economics with far-right migration policies and calls for closer ties to Russia.

Yes, but: The arithmetic may not be enough.

BSW co-chair Amira Mohamed Ali said Sunday the party would neither vote for AfD's Ulrich Siegmund nor CDU Premier Sven Schulze.

Instead, she wants a nonpartisan premier who would govern with BSW and AfD.

This would require support from AfD, but Siegmund rejected the idea.

Siegmund suggested Sunday he may persuade some lawmakers to switch parties to help him secure a majority.

Catch up quick: AfD has won the most votes once before , in 2024, but it has never governed.

In 2024, it finished first in Thuringia, marking the first far-right victory since World War II, but other parties kept it out of government.