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 Holocephali Bonaparte, 1832
                   Superorder Holocephalimorpha Lund, 1986
                     Cochliodontomorpha
                       1 Order †Squalorajiformes Patterson, 1965 [monotypic]
                       2.1.1 Order †Chondrenchelyiformes Moy-Thomas, 1939 [monotypic]
                       2.1.2 Order †Menaspiformes Patterson, 1965
                       2.2.1 Order †Cochliodontiformes Obruchev, 1953
                       2.2.2 Order Chimaeriformes Obruchev, 1953 - chimaeras