There are about twenty recognized clans in Japan. At he peak is the Imperial Clan, i.e. the emperors, although individual emperors did not use a clan name.

Then come the Four Noble Clans (Gempeitōkitsu 源平藤橘). They are the Minamoto, Taira, Fujiwara, and Tachibana Clans. 

Next are the Noble Clans

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There are five clans which are closely related to Shinto as they have hereditarily provided the guji for important jinja. They are the Omi clan of Izumo who provided the guji for Izumo Taisha; the Yamato clan, Oyamoto Jinja; the Aso clan, Aso Jinja; the Owari clan, Atsuta Jina; and the Munakata clan, Munakata Taisha.