Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
514 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 514 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 |
|---|---|---|
| 1. #21462675 | C2 | semidirect |
| 2. #21461278 | C2 | semidirect |
| 3. #21461158 | C2 | semidirect |
| 4. #21461089 | C2 | semidirect |
| 5. #21460684 | C2 | semidirect |
| 6. #21460664 | C2 | semidirect |
| 259. C61 | #9243 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462675 | 2 |
| #21461278 | 2 |
| #21461158 | 2 |
| #21461089 | 2 |
| #21460684 | 2 |
| #21460664 | 2 |
| C2×#16839975 | 2 |
| #9243 | 61 |