Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct. see Subphylum Vertebrata Cuvier, 1812
       Vertebrata (Lamarck, 1801) - vertebrates see Subphylum Vertebrata Cuvier, 1812
         Myopterygii - myopterygians
           Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
             Grade Chondrichthiomorphi
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Elasmobranchii Bonaparte, 1838 - shark-like fishes
                   Infraclass Euselachii Hay, 1902 - sharks and rays, and related fossils
                     Division Neoselachii Compagno, 1977
                       Subdivision Selachii - sharks
                         Superorder Squalomorphi
                           Order Hexanchiformes Compagno, 1973 - six-gill sharks
                             1 Family †Orthacodontidae de Beaumont, 1960 [monotypic]
                             2 Genus †Notidanoides Maisey, 1986
                             3 Genus †Notidanodon Cappetta, 1975
                             4 ?Family †Mcmurdodontidae White, 1968
                             5 Family Chlamydoselachidae Garman, 1884 [monotypic] - frill sharks
                             6 Family Hexanchidae Gray, 1851 - cow sharks