Tridactylidea

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
Ordo: Orthoptera
Subordo: Caelifera
Infraordo: Tridactylidea
Superfamiliae (1 + 1†): Tridactyloidea - †Regiatoidea

Vernacular names
日本語: ノミバッタ下目

The infraorder Tridactylidea[1] has a single extant superfamily which includes pygmy mole crickets; they are thought to represent living representatives of the most basal Caelifera: the Orthopteran suborder that includes grasshoppers.[2]
Superfamilies and Families

The infraorder consists of two superfamilies, one living and one extinct; the Orthoptera Species File lists the following:[3]

†Dzhajloutshelloidea Gorochov, 1994
†Dzhajloutshellidae Gorochov, 1994
†Regiatidae Gorochov, 1995
Tridactyloidea Brullé, 1835
Cylindrachetidae Giglio-Tos, 1914
Ripipterygidae Ander, 1939
Tridactylidae Brullé, 1835

References

Brullé GA (1835) In Audouin & Brullé: Histoire naturelle des insectes 9 [1] (5):1-225 [225–416 in 1836]
Kevan DKM (1982) In Parker [Ed.]: Synopsis and Classification of Living Organisms 2: 378
Orthoptera Species File (Version 5.0/5.0)