Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
374 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 84 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 |
|---|---|---|
| 3. #21461388 | C2 | semidirect |
| 4. #21461386 | C2 | semidirect |
| 5. #21460710 | C2 | semidirect |
| 6. #21460710 | C2 | semidirect |
| 215. C61 | #8863 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462499 | 2 |
| #21461677 | 2 |
| #21461388 | 2 |
| #21461386 | 2 |
| #21460710 | 2 |
| #21444130 | 2 |
| #8863 | 61 |