Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
268 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 86 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 123. C53 | #9634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20290292 | 2 |
| #20290273 | 2 |
| C8×#11719936 | 2 |
| #20289601 | 2 |
| #20273462 | 2 |
| #9634 | 53 |