order or subclass of reptile-like amphibians

Reptiliomorpha is a clade of the amniotes and those tetrapods that share a more recent common ancestor with amniotes than with living amphibians (lissamphibians).

Scientific classification e
Kingdom: Animalia
Phylum: Chordata
Superclass: Tetrapoda
Clade: Reptiliomorpha

Unfortunately, different experts have used the term in several different ways. It has even been used for fossils of early amphibians. It is best used for animals which lay cleidoic eggs, but are not synapsids. Otherwise precursors of reptiles (sauropsids) get lumped together with precursors of mammals (synapsids).

Its only justification is that it may not always be possible to decide which group a fossil is from. But gradually, as with Seymouria, it is possible to separate fossils into more specific grouups.