/*
M22:2 presented on its standard generators.
*/

G<x,y>:=Group<x,y|
x^2,
y^4,
(x*y)^11,
(x*y^2)^6,
(x,y)^4,
// (x*y*x*y^2*x*y^2)^4, // redundant.
(x*y*x*y*x*y^2*x*y^2)^3
>;

c:=x;d:=y;

// Some maximal subgroups of M22:2.
M0:=sub<G|x*y,y^2>; // M22 (triviality).
M1:=sub<G|x,y*x*y^2*x*y^-1*x*y>; // L3(4).2.
M2:=sub<G|x,y*x*y^2*x*y*x*y^2*x*y^-1*x*y^2>; // 2^4:S6.
M5:=sub<G|y^2,x*y*x*y*x*y*x>; // 2^5:S5.
M6:=sub<G|y,x*y*x*y^2*x*y^-1*x>; // 2 x 2^3:L3(2).
M7:=sub<G|x,y*x*y^2*x*y^2>; // Aut(A6).
M8:=sub<G|y^2,y^x>; // PGL2(11).
M34:=sub<G|y^2,x*y*x*y^2*x*y^-1*x*y*x>; // A7, maximal in M22.
M:=[M0,M1,M2,M5,M6,M7,M8,M34];


/*
// Required enumeration even without redundant relation.
11*Index(G,sub<G|x*y>:Print:=2,Hard:=true,Grain:=10^5,CosetLimit:=200000);
*/