  The natural partial ordering of the orbit types of the action of the group of
local gauge transformations on the space of connections in space-time dimension
d<=4 is investigated. For that purpose, a description of orbit types in terms
of cohomology elements of space-time, derived earlier, is used. It is shown
that, on the level of these cohomology elements, the partial ordering relation
is characterized by a system of algebraic equations. Moreover, operations to
generate direct successors and direct predecessors are formulated. The latter
allow to successively reconstruct the set of orbit types, starting from the
principal type.
