Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
486 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 486 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. #20273377 | C2 | semidirect |
| 3. #20272860 | C2 | semidirect |
| 8. #16810416 | C22 | semidirect |
| 10. #16810367 | C22 | semidirect |
| 11. C53×#585 | C4 | semidirect |
| 15. C53×#455 | C4 | semidirect |
| 19. C53×#413 | C4 | semidirect |
| 178. #585 | Dic53 | semidirect |
| 182. #455 | Dic53 | semidirect |
| 187. #413 | Dic53 | semidirect |
| 193. C53 | #13560 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276380 | 2 |
| #20273377 | 2 |
| #20272860 | 2 |
| C53×#3018 | 2 |
| #13560 | 53 |