insol2_23:= [ 
    MatrixGroup<2, GF(23) |
        \[ 0, 1, 22, 1 ],
        \[ 20, 10, 17, 12 ]
        /* order = 12144 = 2^4 * 3 * 11 * 23 */ >,

    MatrixGroup<2, GF(23) |
        \[ 0, 1, 1, 11 ],
        \[ 19, 8, 10, 20 ]
        /* order = 24288 = 2^5 * 3 * 11 * 23 */ >,

    MatrixGroup<2, GF(23) |
        \[ 0, 1, 20, 11 ],
        \[ 3, 21, 5, 5 ]
        /* order = 133584 = 2^4 * 3 * 11^2 * 23 */ >,

    MatrixGroup<2, GF(23) |
        \[ 0, 1, 6, 18 ],
        \[ 11, 15, 22, 11 ]
        /* order = 267168 = 2^5 * 3 * 11^2 * 23 */ >
];