Coloring with reflection orbits

Here are the 24 distinct  four-color colorings of the vertices of a square:

The squares in each one of the six blocks are reflection orbits. These orbits form a partition of the full set of colorings, or, equivalently, a partition of the set of all permutations of  four distinct colors. Can you identify the six orbits?

Last revised 02/02/2011
These  postings are based on "Symmetry Studies An  Introduction to the Analysis of Structured Data in Applications"  Cambridge Press (2008)