G := sub<Sym(14)|(1, 2)(3, 14)(5, 11)(6, 10)(7, 13)(8, 9),(1, 8)(2, 11)(4, 7)(6, 10)(9, 14)(12, 13),(1, 8)(3, 6)(4, 11)(5, 10)(7, 13)(12, 14)>;

involutions :=

[
[
    G!(1, 2)(3, 14)(5, 11)(6, 10)(7, 13)(8, 9),
    G!(1, 8)(2, 11)(4, 7)(6, 10)(9, 14)(12, 13),
    G!(1, 8)(3, 6)(4, 11)(5, 10)(7, 13)(12, 14)
]

];

geometries := [* *];


for i in [1..#involutions] do
	G1 := sub<G|involutions[i][2],involutions[i][3]>;
	G2 := sub<G|involutions[i][1],involutions[i][3]>;
	G3 := sub<G|involutions[i][1],involutions[i][2]>;
	Append(~geometries,CosetGeometry(G,{G1,G2,G3}));
end for;