Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
378 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 378 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #20276474 | C2 | semidirect |
| 5. #20272831 | C2 | semidirect |
| 6. #20272808 | C2 | semidirect |
| 7. C53×#1833 | C2 | semidirect |
| 12. #16810746 | C4 | semidirect |
| 142. #1833 | D53 | semidirect |
| 168. C53 | #12829 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283633 | 2 |
| #20276474 | 2 |
| #20276462 | 2 |
| #20276420 | 2 |
| #20272831 | 2 |
| #20272808 | 2 |
| C53×#1833 | 2 |
| #12829 | 53 |