The group name for rabbit's is a warren. The scientific name would be Oryctolagus Cunciculus. Rabbit's can be classified in many different ways. Their kingdom name is: Animalia. They come from the phylum named: Vertebrata. Their class is: Mammalia. Their order is: Lagomorpha. A rabbit's family name is: Leporidae. Their genus is: Oryctolagus. The species is: Cunciculus.