Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
418 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 80 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. #21461394 | C2 | semidirect |
| 4. #21461392 | C2 | semidirect |
| 5. #21460714 | C2 | semidirect |
| 6. #21460714 | C2 | semidirect |
| 227. C61 | #8864 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462673 | 2 |
| #21461944 | 2 |
| #21461394 | 2 |
| #21461392 | 2 |
| #21460714 | 2 |
| #21444138 | 2 |
| #8864 | 61 |