AULISCOCYATHOIDEA Debrenne & Zhuravlev, 1992: Outer wall simple.
SYRINGOCNEMOIDEA Taylor, 1910: Outer wall concentrically porous.
KRUSEICNEMOIDEA Debrenne & Zhuravlev, 1990: Outer wall pustular.
FRAGILICYATHOIDEA Belyaeva, 1975: Outer wall with canals.