Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
482 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 482 conjugacy classes of subgroups — too many to draw. Only its 79 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. #20276380 | C2 | semidirect |
| 2. #20273350 | C2 | semidirect |
| 3. #20272866 | C2 | semidirect |
| 7. #16810418 | C22 | semidirect |
| 10. #16810363 | C22 | semidirect |
| 11. C53×#585 | C4 | semidirect |
| 14. C53×#456 | C4 | semidirect |
| 19. C53×#413 | C4 | semidirect |
| 178. #585 | Dic53 | semidirect |
| 181. #456 | Dic53 | semidirect |
| 187. #413 | Dic53 | semidirect |
| 193. C53 | #13570 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276380 | 2 |
| #20273350 | 2 |
| #20272866 | 2 |
| C53×#3018 | 2 |
| #13570 | 53 |