Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
616 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 11. C23×Q8×C53 | C4 | semidirect |
| 18. C53×#385 | C4 | semidirect |
| 19. C53×#380 | C4 | semidirect |
| 27. #13133132 | Q8 | semidirect |
| 180. C23×Q8 | Dic53 | semidirect |
| 190. #385 | Dic53 | semidirect |
| 191. #380 | Dic53 | semidirect |
| 195. C53 | #13296 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274707 | 2 |
| C4×#13133132 | 2 |
| #20272833 | 2 |
| C53×#2409 | 2 |
| #13296 | 53 |