C2 x S4 x S3
r0 := (1,2)(3,5)(4,7)(6,9)(8,11)(10,14)(12,15)(13,17)(16,18);
r1 := (1,3)(2,4)(6,10)(8,12)(9,13)(11,16)(14,18)(15,17);
r2 := (3,6)(4,8)(5,9)(7,11)(10,15)(12,14);
r3 := (3,4)(5,7)(6,8)(9,11)(13,16)(17,18);
F := FreeGroup(4);
r0 := F.1;; r1 := F.2;; r2 := F.3;; r3 := F.4;;
G := F/[ r2^2, r3^2, r0^2, r1^2, (r0*r3)^2, (r0*r2)^2, (r3*r2)^2, (r1*r3*r1*r2)^2, r1*r3*r1*r0*(r1*r3)^2*r0, (r1*r2*r1*r0*r2)^2, ((r1*r0)^2*r1*r2)^2, (r0*r1*r3*(r0*r1)^2)^2 ];;
type 0: 6 elements
type 1: 36 elements
type 2: 6 elements
type 3: 4 elements