Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
462 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 89 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. #20277519 | C2 | semidirect |
| 4. #20273318 | C2 | semidirect |
| 6. #20272581 | C2 | semidirect |
| 7. C53×#1285 | C2 | semidirect |
| 10. #16811032 | C4 | semidirect |
| 11. #16810988 | C4 | semidirect |
| 198. #1285 | D53 | semidirect |
| 228. C53 | #9382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20285907 | 2 |
| #20277519 | 2 |
| #20275633 | 2 |
| #20273318 | 2 |
| #20273263 | 2 |
| #20272581 | 2 |
| C53×#1285 | 2 |
| #9382 | 53 |