What is the largest (by large I mean most general) clade of organisms that has gone extinct?
domain > kingdom > phylum > class > order > family > genus > species
So, for example, an extinct kingdom would be larger than an extinct class.
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.
Trilobites ( /ˈtraɪləˌbaɪt, ˈtrɪ-, -loʊ-/; 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.