Largest extinct clade?
Semantics aside, I think the OP wants a group of animals which are  grouped together as related and which are extinct.  I propose trilobites.  They are no more but at one time they ruled the earth.  

from https://en.wikipedia.org/wiki/Trilobite


  Trilobites ( /ˈtraɪləˌbaɪt, ˈtrɪ-, -loʊ-/;[2][3] meaning "three
  lobes") are a fossil group of extinct marine arachnomorph arthropods
  that form the class Trilobita. Trilobites form one of the earliest
  known groups of arthropods. The first appearance of trilobites in the
  fossil record defines the base of the Atdabanian stage of the Early
  Cambrian period (521 million years ago), and they flourished
  throughout the lower Paleozoic era before beginning a drawn-out
  decline to extinction when, during the Devonian, all trilobite orders
  except the Proetids died out. Trilobites disappeared in the mass
  extinction at the end of the Permian about 252 million years ago. The
  trilobites were among the most successful of all early animals,
  roaming the oceans for over 270 million years.[4]