Let n be a positive integer, q be a prime power, and V be a vector space of dimension n over F q . Let G := V rtimes G 0 , where G 0 is an irreducible subgroup of G L ( V ) which is maximal by inclusion with respect to being intransitive on the set of nonzero vectors. We are interested in the class of all diameter two graphs Γ that admit such a group G as an arc-transitive, vertex-quasiprimitive subgroup of automorphisms. In particular, we consider those graphs for which G 0 is a subgroup of either Γ L(n,q) or Γ Sp( n , q ) and is maximal in one of the Aschbacher classes C i , where i ∈ {2, 4, 5, 6, 7, 8} . We are able to determine all graphs Γ which arise from G 0 ≤ Γ L( n , q ) with i ∈ {2, 4, 8} , and from G 0 ≤ Γ Sp( n , q ) with i ∈ {2, 8} . For the remaining classes we give necessary conditions in order for Γ to have diameter two, and in some special subcases determine all G -symmetric diameter two graphs.