CAPSULOCYATHINA Zhuravleva, 1964: Cup single chambered and subspherical, or multichambered without septa.
CRYPTOPOROCYATHIDAE Zhuravleva, 1960: Outer wall with simple pores.
URALOCYATHELLIDAE Zhuravleva, 1964: Outer wall with independent microporous sheath.
TYLOCYATHIDAE Zhuravlev, 1988: Outer wall with attached microporous sheath.
FRANSUASAECYATHIDAE Debrenne, 1964: Outer wall with simple tumuli.
TUBERICYATHIDAE Debrenne, Rozanov, & Zhuravlev, 1989: Outer wall with bracts or scales.