Graphs with projective suborbits. Exceptional cases of characteristic 2. III

This paper is the third in a series in which we complete the description of the finite vertex stabilizers for connected graphs with projective suborbits and, as a corollary, of the vertex stabilizers for finite connected graphs in groups of automorphisms that act transitively on 2-arcs. In this part we complete the treatment of the collineation case under the assumption that the projective dimension of the suborbit is equal to 4.