Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
810 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 176 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. #21462548 | C2 | semidirect |
| 2. #21462546 | C2 | semidirect |
| 3. #21461957 | C2 | semidirect |
| 4. #21461955 | C2 | semidirect |
| 5. #21461811 | C2 | semidirect |
| 6. #21461808 | C2 | semidirect |
| 7. #21461744 | C2 | semidirect |
| 8. #21461537 | C2 | semidirect |
| 28. #16840143 | C4 | semidirect |
| 29. #16840141 | C4 | semidirect |
| 30. #16840138 | C4 | semidirect |
| 31. #16840135 | C4 | semidirect |
| 33. C61×#492 | C4 | semidirect |
| 193. #492 | #6923 | semidirect |
| 208. C61 | #22282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462548 | 2 |
| #21462546 | 2 |
| #21461957 | 2 |
| #21461955 | 2 |
| #21461811 | 2 |
| #21461808 | 2 |
| #21461744 | 2 |
| #21461537 | 2 |
| #21456242 | 2 |
| #22282 | 61 |