Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
410 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 112 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 |
|---|---|---|
| 58. #13133135 | C8 | semidirect |
| 191. C53 | #8836 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20291610 | 2 |
| #20290885 | 2 |
| #20290268 | 2 |
| #20290266 | 2 |
| #20289548 | 2 |
| #20274510 | 2 |
| #8836 | 53 |