Classification

Domain: Eukarya
Kingdom: Animalia
Phylum: Chordata
Class: Mammalia
Order: Perissodactyla
Family: Hyracodontidae
Genus: Paraceratherium
Species: P. bugtiense, P. transouralicum, P. pronorovi, P. orgosensis, P. zhajremenisis
 
Domain: Eukarya - Members that are included in this domain all have a true nucleus, containing the DNA, and they also have membrane bound organelles.  To learn about another eukaryote click here.
 
Kingdom: Animalia - The Paraceratherium is in this kingdom because it is multicellular, heterotrophic, and has internal digestion.  To learn about another organism in the kingdom Animalia click here and here.
 
Phylum: Chordata - The members of this phylum all have a dorsal nerve cord.  To learn about another animal in the phylum Chordata click here or here.
 
Class: Mammalia -  In this class the females nurse all of their offspring with milk from the mammary glands.  To learn about another animal in the class Mammalia click here.
 
Order: Perissodactyla - This order includes non-ruminant ungulates that have an odd number of toes. Non-ruminant ungulates means that it is an animal that does not have a four chambered stomach and they are hooved.  To learn about another animal in the order Perissodactyla click here.
 
Family: Hyracodontidae -  Belonging to this family means that the animal has long limbs and no horns.
 
Genus: Paraceratherium - Near the hornless beast (Prothero 2013).  

Looking at this phylogenetic tree of the Paraceratherium, it is labeled under the name Indricotheriidae.

As you can see, the Paraceratherium is a close relative of the Rhinoceros.