Stauromedusae Haeckel, 1879
Anaconularia Sinclair, 1952
Calloconularia Sinclair, 1952
Conularia Sowerby, 1821
Diconularia Sinclair, 1952
Exoconularia Sinclair, 1952
Flectoconularia Waterhouse, 1979
Gondaconularia Waterhouse, 1986
Metaconularia Foerste, 1928
Notoconularia Thomas, 1969
Paraconularia Sinclair, 1940
