K-3,K-3-free intersection graphs of finite groups

The intersection graph of a group G is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper non-trivial subgroups of G, and there is an edge between two distinct vertices H and K if and only if H boolean AND K not equal 1 where 1 denotes the trivial subgroup of G. In this paper we classify all finite groups whose intersection graphs are K-3,K-3-free.