Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
474 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 474 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. #21462660 | C2 | semidirect |
| 2. #21461278 | C2 | semidirect |
| 3. #21461152 | C2 | semidirect |
| 4. #21461089 | C2 | semidirect |
| 5. #21460725 | C2 | semidirect |
| 6. #21460703 | C2 | semidirect |
| 240. C61 | #9349 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462660 | 2 |
| #21461278 | 2 |
| #21461152 | 2 |
| #21461089 | 2 |
| #21460725 | 2 |
| #21460703 | 2 |
| #21455312 | 2 |
| #9349 | 61 |