First of all, to to those that don't know much about taxonomy, this is how everything works together. Taxonomy is scientists' method of ordering all living things. The taxonomic groups go in this order: kingdom, phylum, class, order, family, genus, and species name.
Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Lagomorpha
Family: Leporidae
Genus: Oryctolagus
Species: Cuniculus (domestic rabbit)
Rabbits belong to the order Lagomorpha, and rodents belong to the order Rodentia. The name Lagomorpha comes from the Latin word lagosmeaning "hare", and morphe meaning "form". The order has only two families: Leporidae (rabbits and hares), and Ochotonidae (pikas).
Just for reference here is what a guinea pig is
Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Rodentia*
Suborder: Hystricomorpha
Family: Caviidae
Subfamily: Caviinae
Genus: Cavia
Species: Cavia porcellus
And rats:
Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Rodentia
Family: Muridae
Genus: Rattus
Species: norvegicus
and hamsters
Kingdom:Animalia
Phylum:Chordata
Subphylum:Vertebrata
Class:Mammalia
Order:Rodentia
Suborder:Myomorpha
Superfamily:Muroidea
Family: Cricetidae
Subfamily: Cricetinae
Genus:
Mesocricetus
Phodopus
Cricetus
Cricetulus
Allocricetulus
Cansumys
Tscherskia