Given a locally compact group, its set of closed subgroups can be endowed with a compact, Hausdorff topology. With this topology, it is called the Chabauty space of the group. Every group acts on its Chabauty space via conjugation. This action has connections to rigidity theory, Margulis' normal subgroup theorem and measure preserving actions of the group via so-called Invariant Random Subgroups (IRS).