Strongly regular graphs are highly symmetrical and can be described fully with just a few parameters, yet the existence of many of them is still under the question. In this paper, we continue the study of the famuly of strongly regular graphs with parameters $λ=1$ and $μ=2$ and establish all of their possible Hamiltonian subgraphs of order seven. By doing so we establish the lower and upper bounds for number of 7-gons, or 7-cycles, in such graphs.