Gauge Orbit Types for Theories with Gauge Group O(n), SO(n) or Sp(n)

We determine the orbit types of the action of the group of local gauge transformations on the space of connections in a principal bundle with structure group O(n), SO(n) or Sp(n) over a closed, simply connected manifold of dimension 4. On the way we derive a classification of Howe subgroups of SO(n) up to conjugacy.