Diadectids and Diadectomorpha are basal lepidosauromorph reptiles once thought to be the closest anamniotes (amphibians) to amniotes. Wikipedia still promotes this antiquated hypothesis. Here (Fig. 1) you’ll see that Diadectes and Procolophon both evolved from a sister to Romeria primus as recovered by the large reptile tree.

Figure 1. The evolution of Diadectes and Procolophon from tiny Romeria primus to scale. Cope’s Rule is in effect here as the derived taxa are indeed larger, even on the branch leading to Procolophon.
Today we’ll look at a humpback diadectid, Diadectes (formerly Diasparactus) zenos (UC679). You’ll note the neural spines are much larger than in sister taxa.

Figure 2. Diadectes (Diasparactus) zenos to scale with other Diadectes specimens. Note the long neural spines. These were likely a hump support, not a finback, adding bulk to this already bulky reptile.
The high neural spines of D. zenos were robust, more like those of a bison, than a Dimetrodon. That’s why they may have supported fatty or meaty tissues, rather than a sail.
The skull of D. zenos is poorly known, but the palate is well exposed. The dorsal ribs are short, as is the tail. Note that the axis bone (cervical #2) grows from D. zenos to D. sammiguelensis (Fig. 2).
Earlier we looked at a putative diadectid, Stephanospondylus, which is actually a diadectid mimic that was ancestral to turtles. It had no neural spines, and neither do turtles, because they don’t need back muscles when they have a shell.
The anterior dorsal ribs of D. zenos were the widest among diadectids. These helped support that large pectoral girdle.
Please contact the writer(s) of the Wikipedia article and encourage them to update their account of Diadectes. You can’t be derived from reptiles and still be a ‘reptile-like amphibian.’
References
Berman DS, Sumida SS and Martens T 1998. Diadectes (Diadectomorpha: Diadectidae) from the Early Permian of central Germany, with description of a new species. Annals of Carnegie Museum 67:53-93.
Case EC 1907. Restoration of Diadectes. The Journal of Geology 15(6):556–559.
Case EC 1910.“New or little known reptiles and amphibians from the Permian (?) of Texas”. Bulletin of the American Museum of Natural History 28:136–181.
Case EC, Williston SW and Mehl MG 1913. Permo-Carboniferous Vertebrates from New Mexico. Carnegie Institution. 81 pp. online pdf
Cope ED 1878a. Descriptions of extinct Batrachia and Reptilia from the Permian formation of Texas. Proceedings of the American Philosophical Society 17:505-530.
Cope ED 1878b. A new Diadectes. The American Naturalist 12:565.
Kissel R 2010. Morphology, Phylogeny, and Evolution of Diadectidae (Cotylosauria: Diadectomorpha). Thesis (Graduate Department of Ecology & Evolutionary Biology University of Toronto).
Wiki/Diadectes