A construction of all normal subgroup lattices of 2-transitive automorphism groups of linearly ordered sets

We give a complete classification and construction of all normal subgroup lattices of 2-transitive automorphism groups A(Ω) of linearly ordered sets (Ω, ≦). We also show that in each of these normal subgroup lattices, the partially ordered subset of all those elements which are finitely generated as normal subgroups forms a lattice which is closed under even countably-infinite intersections, and we derive several further group-theoretical consequences from our classification.