Which communities do not allow women to drive cars?
I know the Belzer hassidim do not allow this, but I do not know about any other communities.
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I have found the answer. The Shulchan Aruch (73:1) and Rambam states that a woman shouldn't leave the house too much. And of course, you have Shevet haLevi 4:1:2. Apparently, humras regarding tznius are recommended by Rashi.
It seems that Belz, Satmar, Viznitz, Skver, Bobov and Pupa do not allow this. But I don't know whether this is official or just an implicit minhag, nor whether it's universal in those groups.