Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
612 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 612 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 |
| 24. #13133134 | Q8 | semidirect |
| 182. C23×Q8 | Dic53 | semidirect |
| 192. #385 | Dic53 | semidirect |
| 194. #380 | Dic53 | semidirect |
| 197. C53 | #13293 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20274703 | 2 |
| C4×#13133134 | 2 |
| #20272833 | 2 |
| C53×#2409 | 2 |
| #13293 | 53 |