Normal 2-coverings in affine groups of small dimension

A finite group G admits a normal 2-covering if there exist two proper subgroups H and K with G=∪g∈GHg∪∪g∈GKg. For determining inductively the finite groups admitting a normal 2-covering, it is important to determine all finite groups G possessing a normal 2-covering, where no proper quotient of G admits such a covering. Using terminology arising from the O’Nan-Scott theorem, Garonzi and Lucchini have shown that these groups fall into four natural classes: product action, almost simple, affine and diagonal. In this paper, we start a preliminary investigation of the affine case.