Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
404 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 81 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. #20276187 | C2 | semidirect |
| 4. #20272538 | C2 | semidirect |
| 5. #20272537 | C2 | semidirect |
| 7. C53×#2099 | C2 | semidirect |
| 180. #2099 | D53 | semidirect |
| 213. C53 | #7799 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20281675 | 2 |
| #20276187 | 2 |
| #20276119 | 2 |
| #20272538 | 2 |
| #20272537 | 2 |
| #20272535 | 2 |
| C53×#2099 | 2 |
| #7799 | 53 |