Odonatoptera

The Odonatoptera are a superorder (sometimes treated as an order) of ancient flying insects.
It includes all kinds of dragonflies, and is placed in the Palaeoptera. 
The dragonflies and damselflies are the only living members of this group. It was far more diverse in the late Paleozoic and contained gigantic species, including the griffinflies (or "giant dragonflies") of the order Protodonata. This lineage dates back at least to the Pennsylvanian, not quite 320 million years ago. 
It is now clear that giant dragonflies survived to the end of the Permian.