Finite Group DatabasebetaFinite Group DatabasebetaOrder 13568.
416 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 416 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. #20283810 | C2 | semidirect |
| 2. #20273227 | C2 | semidirect |
| 5. #20272577 | C2 | semidirect |
| 6. #20272543 | C2 | semidirect |
| 22. C53×#494 | C4 | semidirect |
| 23. C53×#492 | C4 | semidirect |
| 24. C53×#487 | C4 | semidirect |
| 25. C53×#486 | C4 | semidirect |
| 177. #494 | Dic53 | semidirect |
| 178. #492 | Dic53 | semidirect |
| 179. #487 | Dic53 | semidirect |
| 180. #486 | Dic53 | semidirect |
| 196. C53 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20283810 | 2 |
| #20273227 | 2 |
| #20273223 | 2 |
| #20273184 | 2 |
| #20272577 | 2 |
| #20272543 | 2 |
| C53×#3210 | 2 |
| #9282 | 53 |