Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
464 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 103 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. #20276407 | C2 | semidirect |
| 2. #20276365 | C2 | semidirect |
| 3. #20274765 | C2 | semidirect |
| 4. #20274515 | C2 | semidirect |
| 15. C22×D8×C53 | C4 | semidirect |
| 22. C53×#427 | C4 | semidirect |
| 23. C53×#418 | C4 | semidirect |
| 172. C22×D8 | Dic53 | semidirect |
| 180. #427 | Dic53 | semidirect |
| 181. #418 | Dic53 | semidirect |
| 190. C53 | #13234 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20276407 | 2 |
| #20276365 | 2 |
| #20274765 | 2 |
| #20274515 | 2 |
| C53×#3058 | 2 |
| #13234 | 53 |