Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
534 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 534 conjugacy classes of subgroups — too many to draw. Only its 96 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. #21462011 | C2 | semidirect |
| 3. #21461376 | C2 | semidirect |
| 4. #21461332 | C2 | semidirect |
| 6. #21461028 | C2 | semidirect |
| 185. C8×C61 | #100 | semidirect |
| 187. #92418 | #100 | semidirect |
| 247. C61 | #9805 | semidirect |
| 404. C8 | #14519837 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462011 | 2 |
| #21461961 | 2 |
| #21461376 | 2 |
| #21461332 | 2 |
| #21461326 | 2 |
| #21461028 | 2 |
| C2×#16840133 | 2 |
| #9805 | 61 |