Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
406 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 406 conjugacy classes of subgroups — too many to draw. Only its 78 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. #21462178 | C2 | semidirect |
| 2. #21461382 | C2 | semidirect |
| 3. #21460832 | C2 | semidirect |
| 4. #21460831 | C2 | semidirect |
| 7. #16840683 | C22 | semidirect |
| 11. #16840624 | C22 | semidirect |
| 185. C61 | #11957 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462178 | 2 |
| #21461382 | 2 |
| #21460832 | 2 |
| #21460831 | 2 |
| #495×D61 | 2 |
| #11957 | 61 |