Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 94 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. #21462012 | C2 | semidirect |
| 3. #21461373 | C2 | semidirect |
| 4. #21461334 | C2 | semidirect |
| 6. C8×#11758217 | C2 | semidirect |
| 228. C61 | #9800 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462012 | 2 |
| #21461961 | 2 |
| #21461373 | 2 |
| #21461334 | 2 |
| #21461326 | 2 |
| C8×#11758217 | 2 |
| C2×#16840107 | 2 |
| #9800 | 61 |