Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
450 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 122 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. #21462025 | C2 | semidirect |
| 2. #21461366 | C2 | semidirect |
| 3. #21460777 | C2 | semidirect |
| 7. #16840651 | C22 | semidirect |
| 10. #16840623 | C22 | semidirect |
| 45. C2×D8×C61 | C8 | semidirect |
| 149. C61 | #11599 | semidirect |
| 154. C2×D8 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462025 | 2 |
| #21461366 | 2 |
| #21460777 | 2 |
| C2×D8×Dic61 | 2 |
| #11599 | 61 |