Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
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. #21454914 | C2 | semidirect |
| 2. #21444331 | C2 | semidirect |
| 5. #21443681 | C2 | semidirect |
| 6. #21443647 | C2 | semidirect |
| 22. C61×#494 | C4 | semidirect |
| 23. C61×#492 | C4 | semidirect |
| 24. C61×#487 | C4 | semidirect |
| 25. C61×#486 | C4 | semidirect |
| 177. #494 | Dic61 | semidirect |
| 178. #492 | Dic61 | semidirect |
| 179. #487 | Dic61 | semidirect |
| 180. #486 | Dic61 | semidirect |
| 196. C61 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454914 | 2 |
| #21444331 | 2 |
| #21444327 | 2 |
| #21444288 | 2 |
| #21443681 | 2 |
| #21443647 | 2 |
| C61×#3210 | 2 |
| #9282 | 61 |