Phylum Chordata Bateson, 1885 - chordates
   Subphylum Vertebrata Cuvier, 1812 - vertebrates
     Pisces
       Class Chondrichthyes Huxley, 1880 - cartilaginous fishes
         Subclass Holocephali Bonaparte, 1832
           Order Chimaeriformes Obruchev, 1953 - chimaeras
           Order †Chondrenchelyiformes Moy-Thomas, 1939
           Order †Copodontiformes Obruchev, 1953
           Order †Edestiformes see Order Eugeneodontiformes Zangerl, 1981
           Order †Helodontiformes Patterson, 1965
           Order †Iniopterygiformes Zangerl & Case, 1973
           Order †Myriacanthiformes see Suborder Myriacanthoidei Patterson, 1965
           Order †Petalodontiformes Zangerl, 1981
           Order †Psammodontiformes Obruchev, 1953