Metapterygota

Superregnum: Eukaryota
Cladus: Unikonta
Cladus: Opisthokonta
Cladus: Holozoa
Regnum: Animalia
Subregnum: Eumetazoa
Cladus: Bilateria
Cladus: Nephrozoa
Cladus: Protostomia
Cladus: Ecdysozoa
Cladus: Panarthropoda
Phylum: Arthropoda
Subphylum: Hexapoda
Classis: Insecta
Cladus: Dicondylia
Subclassis: Pterygota
Cladus: Metapterygota
Cladi: Neoptera - Odonatoptera - †Palaeodictyopterida
[list of cladi adapted from Grimaldi & Engel (2005: 147, table 4.1)]
Overview of ordines

Blattodea - Coleoptera - Dermaptera - Diptera - Embiidina - Hemiptera - Hymenoptera - Isoptera - Lepidoptera - Mantodea - Mecoptera - Megaloptera - Neuroptera - Notoptera - Odonata - Orthoptera - Phasmatodea - Phthiraptera - Plecoptera - Psocoptera - Raphidioptera - Siphonaptera - Strepsiptera - Thysanoptera - Trichoptera - Zoraptera – †Skleroptera

Name

Metapterygota Börner, 1909
References

Grimaldi, D.; Engel, M.S. 2005: Evolution of the insects. Cambridge University Press, New York, USA. limited preview on Google books

Metapterygota is a clade of winged insects containing order Odonata and Infraclass Neoptera. They share morphological characteristics of a loss of caudal filiaments and a subimago stage. Genetically the clade is supported by similarities in the mitochondrial genomes. [1]
Living Subgroups

Odonatoptera
Odonata
Neoptera
Exopterygota
Endopterygota (=Metabola or Holometabola)

Phylogeny

Insecta

Monocondylia    Archaeognatha      Dicondylia   Apterygota    Zygentoma     †Monura      Pterygota    Ephemeroptera   Metapterygota   Odonata     Neoptera

 
 
References

Yeates, David K; Cameron, Stephen L; Trautwein, Michelle (May 2012). "A view from the edge of the forest: recent progress in understanding the relationships of the insect orders: The relationships of the insect orders". Australian Journal of Entomology. 51 (2): 79–87. doi:10.1111/j.1440-6055.2012.00857.x.