Phylum Chordata Bateson, 1885 - chordates Subphylum Vertebrata Cuvier, 1812 - vertebrates Class Mammalia Linnaeus, 1758 - mammals Order Cetacea Brisson, 1762 - whales, dolphins, and porpoises see Infraorder Cetacea Brisson, 1762 Family Ziphiidae Gray, 1850 - beaked whales