Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
312 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 97 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 |
|---|---|---|
| 3. #20276311 | C2 | semidirect |
| 5. #20275506 | C2 | semidirect |
| 6. #20272831 | C2 | semidirect |
| 7. C53×#1382 | C2 | semidirect |
| 15. #16810438 | C4 | semidirect |
| 16. #16810435 | C4 | semidirect |
| 142. #1382 | D53 | semidirect |
| 165. C53 | #13146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276462 | 2 |
| C2×#16810431 | 2 |
| #20276311 | 2 |
| #20275611 | 2 |
| #20275506 | 2 |
| #20272831 | 2 |
| C53×#1382 | 2 |
| #13146 | 53 |