Pleurodira is the group that consists of all turtles who wrap their necks around their shell. They wrap their necks around because they are too long to fit inside of their shell like the turtles in Cryptodira. They are usually called "side-necked" or "snake-necked" turtles because of how long their necks usually are (I'll add images in the future). There are no more clade-specific groups anymore, so you will no longer see my lists of notable clade-only members. But that is good because you can quickly move through the hyperlinks! Also, from here, the main source of debate is over Linnaean vs PhyloCode classification. I will do my best to keep track of both, but I will default to Linnaean if I need to! (Again, if you see a problem or any misinformation, send a DM to me in Discord)
There are a lot less Pleurodirans (I think that is a real word? Maybe I just made it up...) then Cryptodirans (I'm going to make these real words!), so Pleurodira branches off into 2 Superfamilies (one step down from an Infraorder). And, again, there are some sources that have it as 3, but they are so obscure that I'm just going to ignore them for this site (I'll make a note of which one was dropped down in their designated folder):
Cheloidea (Called Chelidae in PhyloCode)
Pelomedusoidea (Called Pelomedusoides in PhyloCode)