Permothemistida is an extinct order of palaeozoic paleopterous insects.
The order was originally named Permothemistida by Martynov (1938), synonymized with Palaeodictyoptera by Carpenter (1992) and replaced by the name Dicliptera in 2005 by Grimaldi and Engel.
Dicliptera is still used as a name for the order in 2019.
The family Diathemidae, containing the species "Diathema concinnum" and "Diathema tenerum" have been assigned to Permothemistida/ Dicliptera.