Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1016 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 224 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. #21462663 | C2 | semidirect |
| 2. #21462391 | C2 | semidirect |
| 3. #21461289 | C2 | semidirect |
| 4. #21461284 | C2 | semidirect |
| 5. #21461274 | C2 | semidirect |
| 6. #21461269 | C2 | semidirect |
| 204. C61 | #17655 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462663 | 2 |
| #21462391 | 2 |
| #21461289 | 2 |
| #21461284 | 2 |
| #21461274 | 2 |
| #21461269 | 2 |
| #21459820 | 2 |
| #17655 | 61 |