Of course, like any category, it has a skeleton, but as usually defined it is not itself skeletal, since there can exist distinct subgroups and such that .
Warning: This should not be confused with the situation where a group acts on a groupoid so that one obtains the orbit groupoid.
More generally, given a family of subgroups of which is closed under conjugation and taking subgroups one looks at the full subcategory whose objects are those for which .
Sometimes a family, , of subgroups is specified, and then a subcategory of consisting of the where will be considered. If the trivial subgroup is in then many of the considerations of results such as Elmendorf's theorem will go across to the restricted setting.