Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 456 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 |
|---|---|---|
| 2. #21461281 | C2 | semidirect |
| 4. #21461092 | C2 | semidirect |
| 5. #21460684 | C2 | semidirect |
| 6. #21460664 | C2 | semidirect |
| 236. C61 | #9245 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462675 | 2 |
| #21461281 | 2 |
| #21461158 | 2 |
| #21461092 | 2 |
| #21460684 | 2 |
| #21460664 | 2 |
| C2×#16840060 | 2 |
| #9245 | 61 |