The infraclass of mammals which includes all the placental mammals; as opposed to the monotremes and the marsupials

Infraclass Eutheria (Placentalia)

Order Xenarthra - anteaters, sloths, and armadillos; 29 species
Order Insectivora - shrews, tenrecs, moles, hedgehogs; 429 species
Order Scandentia - tree shrews; 19 species
Order Dermoptera - Colugos; 2 species
Order Chiroptera - Bats; 928 species
Order Primates - lemurs, monkeys and apes; 236 species
Order Carnivora - cats, dogs, bears, seals, raccoons etc.; 271 species
Order Cetacea - whales and dolphins; 78 species
Order Sirenia - dugongs and manatees; 5 species
Order Proboscidea - elephants; 2 species
Order Hyracoidea - hyraxes; 6 species
Order Perissodactyla - horses, tapirs and rhinos; 18 species
Order Tubulidentata - Aardvark; 1 species
Order Artiodactyla - pigs, hippos, camels, bovids, antelopes, deer; 220 species
Order Pholidota - pangolins; 7 species
Order Rodentia - rodents; 2024 species
Order Lagomorpha - hares, rabbits and pikas; 80 species
Order Macroscelidea - elephant shrews; 15 species

Source: Mammalogy 4th edition; by Terry A. Vaughan, James M. Ryan, and Nicholas J. Czaplewski