COSCINOCYATHOIDEA Taylor, 1910: Outer wall tabular with simple pores.
CALYPTOCOSCINOIDEA Debrenne, 1964: Outer wall tabular with independent microporous sheath.
ALATAUCYATHOIDEA Zhuravleva, 1955: Outer wall tabular with multiperforate tumuli.
CLATHRICOSCINOIDEA Rozanov, 1964: Outer wall tabular and pseudoclathrate.