Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
1168 conjugacy classes of subgroups; only the 139 normal subgroups are shown.
This group has 1168 conjugacy classes of subgroups — too many to draw. Only its 139 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×#16810410 | C2 | semidirect |
| 2. #20274643 | C2 | semidirect |
| 3. #20274633 | C2 | semidirect |
| 13. C23×D4×C53 | C4 | semidirect |
| 19. C2×#120×C53 | C4 | semidirect |
| 21. C2×#117×C53 | C4 | semidirect |
| 216. C23×D4 | Dic53 | semidirect |
| 222. C2×#120 | Dic53 | semidirect |
| 224. C2×#117 | Dic53 | semidirect |
| 232. C53 | #12691 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16810410 | 2 |
| #20274643 | 2 |
| #20274633 | 2 |
| C2×C53×#535 | 2 |
| #12691 | 53 |