SALAIROCYATHOIDEA Zhuravleva, 1956: Outer wall with simple pores.
KASYRICYATHOIDEA Zhuravleva, 1961: Outer wall with independent microporous sheath.
POLYCOSCINOIDEA Debrenne, 1964: Outer wall with attached microporous sheath.
ETHMOCOSCINOIDEA Zhuravleva, 1957: Outer wall with simple tumuli.
COSCINOPTYCTOIDEA Debrenne, Rozanov, & Zhuravlev, 1989: Outer wall with multiperforate tumuli.
SIGMOCOSCINOIDEA R. Bedford & J. Bedford, 1939: Outer wall with bracts or scales.
POROCOSCINOIDEA Debrenne, 1964: Outer wall with noncommunicating canals.
MOOTWINGEECYATHOIDEA Kruse, 1982: Outer wall clathrate.