Hexapoda, the so-called "True Dragons" (although in my personal opinion, the distingushment from "true dragons" and "non-dragon" dragons is arbitrary), and are classified by having 6 limbs (pelvic, cervical and pectoral) which are all used for various purposes, unlike in the Wyverniformes, which have their pectoral limbs either atrophied or lost.
Polycephala, "many heads". At some point in their evolution, basal Hexapod dragons experienced a mutation called Dicephaly that caused multiple heads to grow from one body. Normally this mutation is a death sentence, but through favourable conditions in their prehistory, this was a mutation that seemed to be selected for, and gradually the Polycephalans emerged (although their earliest ancestors still only had one head). Today, members of the Polycephala are unique for having adaptations suitable for carrying multiple heads on one body.
Phytohydridae
Snaptrapper (Phytohydra muscipula)
Dicephalodraconoidea
Dicephalodraconidae
Hideous Zippleback (Dicephalodrakon moschatus)
Tetanocephalidae, "Stiff Heads", which probably evolved from an ancestor similar to the zippleback, but gained aquatic adaptations and eventually became a marine species of multi-headed Dragon.
Seashocker (Tetanocephalus brontothalassus)
Tipidraconia, "typical dragons" or "average dragons". Some also call these the "true" true dragons.
Felidraconia, characterised largely by their intelligence, large eye sockets, relatively flat faces, and feline mannerisms.
Tetrapteridae, which at some point in their evolutionary history, developed a second pair of wings, likely to provide additional stability during flight.
Stormcutter (Tetrapteryx tytooides)
Adonovenatoridae, meaning "Toothless Hunters"
Woolly Howl (Venatorotherium moschatus)
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Peltosauria, the "Armoured Lizards". They are mainly distinguished from other Tipidraconians by the development of bony armour (Osteoderms). While other Dragon lineages do possess some osteoderm coverage, the Peltosaurians have this feature almost universally.
Dracochoeroidea, the Gronckle-like Dragons, including the lineage that leads to the Gronckle itself.
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Anuroididae, very basal Dracochoeroids.
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Arthroptera, the "jointed wings". This is kind of a misnomer, as these dragons don't actually have arthropod-like joints, but rather very derived osteoderm armour that resembles the exoskeletons of arthropods.
Mantocheiridae
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Pyrodraconia, the typical "Fire Dragons" even though that name is a little bit of a misnomer
Draconidae, the the traditional "Western Dragon" family.
Dracovaraninae, basal Draconids that later diversified to fill squamate niches in the colder temperate & boreal climates
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Draconinae
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Delphinidraconinae
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