Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
726 conjugacy classes of subgroups; only the 192 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 192 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. #21462544 | C2 | semidirect |
| 2. #21461419 | C2 | semidirect |
| 3. #21461378 | C2 | semidirect |
| 4. #21461166 | C2 | semidirect |
| 5. #21461015 | C2 | semidirect |
| 77. D61⋊C8 | D8 | semidirect |
| 162. C61 | #17975 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462544 | 2 |
| #21461419 | 2 |
| #21461378 | 2 |
| #21461166 | 2 |
| #21461015 | 2 |
| #21456399 | 2 |
| #17975 | 61 |