Isomorphism and Subgraphs · Hard problem

Let $G$ have vertices $1,\ldots,6$ and edges $12,23,34,45,56,16$ (a $6$-cycle) together with the chord $25$ joining opposite vertices. How many $4$-cycles (sets of $4$ vertices whose edges can be arranged into a cycle using $4$ of $G$'s edges) does $G$ contain?