Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
360 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 74 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. #21462171 | C2 | semidirect |
| 4. #21461624 | C2 | semidirect |
| 5. #21460895 | C2 | semidirect |
| 6. #21460862 | C2 | semidirect |
| 23. #16839576 | C4 | semidirect |
| 24. #16839575 | C4 | semidirect |
| 25. #16839574 | C4 | semidirect |
| 26. C61×#361 | C4 | semidirect |
| 190. #361 | #6923 | semidirect |
| 194. C61 | #13136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462171 | 2 |
| #21462128 | 2 |
| #21461966 | 2 |
| #21461624 | 2 |
| #21460895 | 2 |
| #21460862 | 2 |
| #361×D61 | 2 |
| #13136 | 61 |