Kingdom Animalia Linnaeus, 1758 - animals
   Phylum Brachiopoda Duméril, 1806 - brachiopods
     Class Inarticulata (Huxley, 1869)
       Order Acrotretida Kuhn, 1949
         Genus †Apsotreta Palmer, 1954
         Genus †Ceratreta Bell, 1941
         Genus †Clistotrema Rowell, 1963
         Genus †Conotreta Walcott, 1890
         Genus †Ephippelasma Cooper, 1956
         Genus †Hadrotreta Rowell, 1966
         Genus †Orbiculoidea d'Orbigny, 1847
         Genus Pelagodiscus Dall, 1908
         Genus †Rhysotreta Cooper, 1956
         Genus †Torynelasma Cooper, 1956
         1 Suborder Acrotretidina Kuhn, 1949 see Order Lingulida Waagen, 1885
         2 Suborder Craniidina Waagen, 1885 see Order Craniida Waagen, 1885