Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
408 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 84 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. #21461756 | C2 | semidirect |
| 2. #21461253 | C2 | semidirect |
| 3. #21461251 | C2 | semidirect |
| 6. #21461033 | C2 | semidirect |
| 24. #16840112 | C4 | semidirect |
| 25. #16840110 | C4 | semidirect |
| 26. #16840109 | C4 | semidirect |
| 30. C61×#487 | C4 | semidirect |
| 204. #487 | #6923 | semidirect |
| 222. C61 | #9758 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461756 | 2 |
| #21461253 | 2 |
| #21461251 | 2 |
| #21461250 | 2 |
| #21461033 | 2 |
| #21456143 | 2 |
| #9758 | 61 |