insol2_7:= [ 
    MatrixGroup<2, GF(7) |
        \[ 0, 1, 6, 0 ],
        \[ 1, 0, 6, 1 ]
        /* order = 336 = 2^4 * 3 * 7 */ >,

    MatrixGroup<2, GF(7) |
        \[ 0, 1, 6, 0 ],
        \[ 1, 0, 0, 6 ],
        \[ 5, 4, 3, 4 ]
        /* order = 672 = 2^5 * 3 * 7 */ >,

    MatrixGroup<2, GF(7) |
        \[ 0, 1, 6, 0 ],
        \[ 2, 0, 0, 2 ],
        \[ 1, 0, 6, 1 ]
        /* order = 1008 = 2^4 * 3^2 * 7 */ >,

    MatrixGroup<2, GF(7) |
        \[ 0, 1, 6, 0 ],
        \[ 1, 0, 0, 6 ],
        \[ 2, 0, 0, 2 ],
        \[ 5, 4, 3, 4 ]
        /* order = 2016 = 2^5 * 3^2 * 7 */ >
];