Actually, "rodent" (Rodentia) is the order, the family name is Muridae, and the genus is Rattus (rat). There are 64 species in the genus, one of which is the widespread Black Rat, or Rattus rattus, whose name literally translates from Latin to "rat rat".
These 64 species are true (taxonomical) rats. There are some rodents that are not taxonomically classified as Rattus (some not even Muridae) but include "rat" in their common name though.
And the scientific name of our chickens is Gallus gallus Which if my high school Latin teacher is to be believed means French french.
In a scientific sense there is no subspecies of chickens because all off types of Gallus gallus all of their off spring are fertile and are not hybrids. The same is not true of all the 64 species of Rattus rattus.
Species: Gallus gallus
Subspecies: Gallus gallus domesticus