†order Cornuta Jaekel 1901
Parent taxon: Stylophora according to G. Ubaghs 1999
Sister taxa: Mitrata, Mitrocystitida
Subtaxa: Acuticarpus, Amygdalotheca, Archaeocothurnus, Babinocystis, Beryllia, Bohemiaecystis, Ceratocystis, Chauvelia, Chauvelicystis, Cothurnocystidae, Cothurnocystis, Cothurnocystisbifida, Domfrontia, Galliaecystis, Hanusia, Lobocarpus, Lyricocarpus, Milonicystis, Nanocarpus, Nevadaecystis, Ovocarpus, Phyllocystis, Prochauvelicystis, Procothurnocystis, Progalliaecystis, Prokopicystis, Protocystites, Reticulocarpos, Scotiaecystis, Thoralicystis
Ecology: facultatively mobile epifaunal suspension feeder