Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
360 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. #20276971 | C2 | semidirect |
| 2. #20276970 | C2 | semidirect |
| 3. #20276964 | C2 | semidirect |
| 4. #20274329 | C2 | semidirect |
| 5. #20274320 | C2 | semidirect |
| 6. #20272631 | C2 | semidirect |
| 7. C53×#2246 | C2 | semidirect |
| 64. C16×C53 | D8 | semidirect |
| 65. #11719908 | D8 | semidirect |
| 101. #2246 | D53 | semidirect |
| 123. C53 | #12519 | semidirect |
| 168. C16 | #11719922 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276971 | 2 |
| #20276970 | 2 |
| #20276964 | 2 |
| #20274329 | 2 |
| #20274320 | 2 |
| #20272631 | 2 |
| C53×#2246 | 2 |
| #12519 | 53 |