exists and is an alternate of . There are many different species of rabbit. Pet rabbits are the species European Rabbit (Oryctolagus cuniculus), and there are many different breeds in this species. Rabbits are not rodents: they belong to the Lagomorph order (Lagomorpha) which includes rabbits, hares, and pikas. Rabbits and hares belong to the Leporid family (Leporidae).