Among the best-known pest species are the American cockroach, Periplaneta americana, which is about 30 mm (1.2 in) long; the German cockroach, Blattella germanica, about 15 mm (0.59 in) long; the Asian cockroach, Blattella asahinai, also about 15 mm (0.59 in) in length; and the Oriental cockroach, Blatta orientalis, about 25 mm (0.98 in). Tropical cockroaches are often much bigger, and extinct cockroach relatives and 'roachoids' such as the Carboniferous Archimylacris and the Permian Apthoroblattina were not as large as the biggest modern species.
Dictyoptera (from Ancient Greek diktuon "net" + pteron "wing") is an insect superorder that includes two orders of polyneopterous insects - the termites and cockroaches (both order: Blattaria) along with the mantids (order: Mantodea). While all modern Dictyoptera have short ovipositors, the oldest fossils of Dictyoptera have long ovipositors, much like members of the Orthoptera.
The use of the term Dictyoptera has changed over the years, and while largely out of use for much of the last century, it is becoming more widely used. It has usually been considered a superorder, with Isoptera, Blattaria and Mantodea being its three orders. In some classifications, however, Dictyoptera is shifted to order status and in others the class Isoptera has been subsumed under Blattaria while retaining Dictyoptera as a superorder. Regardless, in all classifications the constituent groups are the same, just treated at different rank. Termites and cockroaches are very closely related, with ecological and molecular data pointing to a relationship with the cockroach genus Cryptocercus (Lo et al., 2000.).
Based on genetic evidence, the closest living relatives of the Dictyoptera are the phasmids and the enigmatic groups Mantophasmatodea and Grylloblattodea. If the Dictyoptera are considered a superorder these three orders might be included in it (Cameron et al., 2006).