Originally , temnospondyls were classified according to the structure of their vertebrae . Early forms , with complex vertebrae consisting of a number of separate elements , were placed in the suborder Rachitomi , and large Triassic aquatic forms with simpler vertebrae were placed in the suborder Stereospondyli . With the recent growth of phylogenetics , this classification is no longer viable . The basic rhachitomous condition is found in many primitive tetrapods , and is not unique to one group of temnospondyls . Moreover , the distinction between rhachitomous and stereospondylous vertebrae is not entirely clear . Some temnospondyls have rhachitomous , semirhachitomous , and sterospondylous vertebrae at different points in the same vertebral column . Other taxa have intermediate morphologies that do not fit into any category . Rachitomi is no longer recognized as a group , but Stereospondyli is still considered valid . Below is a simplified taxonomy of temnospondyls showing currently recognized groups :