Isomorphism and Subgraphs · Challenge problem

Graph $P$ has vertices $1,\ldots,6$ and edges $12,23,34,45,56,16$ (a $6$-cycle). Graph $Q$ has the same vertices and edges $12,23,13,45,56,46$ (two disjoint triangles). Graph $R$ has vertices $1,\ldots,6$ with all $9$ cross edges between $\{1,2,3\}$ and $\{4,5,6\}$ (i.e. $K_{3,3}$). Graph $T$ has vertices $1,\ldots,6$ and edges $31,15,54,42,26,63$ (read as a cyclic sequence). Among $P,Q,R,T$, how many distinct isomorphism classes are represented?