  We consider here the problem of classifying orbits of an action of the dif-
feomorphism group of 3-space on a tower of fibrations with P2-fibers that
generalize the Monster Tower due to Montgomery and Zhitomirskii. As a corollary
we give the first steps towards the problem of classifying Goursat 2-flags of
small length. In short, we classify the orbits within the first four levels of
the Monster Tower and show that there is a total of 34 orbits at the fourth
level in the tower.
