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. Due to this uncertainty, it is of immense interest to study their structure, in particular to obtain all the possible subgraphs of lower order. In this paper we study the family of strongly regular graphs with parameters $λ=1$ and $μ=2$ and establish all their subgraphs of order six.