Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
492 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 492 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. C2×#16810418 | C2 | semidirect |
| 2. #20273339 | C2 | semidirect |
| 3. #20272866 | C2 | semidirect |
| 8. #16810418 | C22 | semidirect |
| 10. #16810363 | C22 | semidirect |
| 11. C2×2−1+4×C53 | C4 | semidirect |
| 16. C53×#454 | C4 | semidirect |
| 19. C2×#101×C53 | C4 | semidirect |
| 29. 2−1+4×C53 | C2×C4 | semidirect |
| 52. #101×C53 | C2×C4 | semidirect |
| 181. C2×2−1+4 | Dic53 | semidirect |
| 186. #454 | Dic53 | semidirect |
| 190. C2×#101 | Dic53 | semidirect |
| 196. C53 | #13569 | semidirect |
| 200. 2−1+4 | C2×Dic53 | semidirect |
| 225. #101 | C2×Dic53 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810418 | 2 |
| #20273339 | 2 |
| #20272866 | 2 |
| C2×C53×#454 | 2 |
| #13569 | 53 |