Superphylum Deuterostomia Grobben, 1908 - deuterostomes see Infrakingdom Deuterostomia Grobben, 1908
   Phylum Chordata Bateson, 1885 - chordates
     Subphylum Craniata auct.
       Infraphylum Vertebrata Lamarck, 1801 - vertebrates
         Superclass Gnathostomata Gegenbaur, 1874 - jawed vertebrates
           Eugnathostomata
             Grade Chondrichthyomorphi [monotypic]
               Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
                 Subclass Euselachii Hay, 1902 - sharks, rays, and related fossils
                   Infraclass Elasmobranchii Bonaparte, 1838
                     Division Selachii - sharks
                       Superorder Squalomorphi
                         Series Hexanchida [monotypic]
                           Order Hexanchiformes Compagno, 1973 - six-gill sharks
                             1 Family †Orthacodontidae Glickman, 1957 see Family Palaeospinacidae Regan, 1906
                             2 Family †Paraorthacodontidae Klug, 2010 see Family Palaeospinacidae Regan, 1906
                             3 Family †Pseudonotidanidae Underwood & Ward, 2004
                             4 Family Chlamydoselachidae Garman, 1884 - frill sharks
                             5 Family Hexanchidae Gray, 1851 - cow sharks