Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
422 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 102 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. #21462180 | C2 | semidirect |
| 2. #21462176 | C2 | semidirect |
| 3. #21460770 | C2 | semidirect |
| 6. C4⋊#11758187 | C22 | semidirect |
| 10. C4×#11758187 | C22 | semidirect |
| 146. C61 | #11631 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462180 | 2 |
| #21462176 | 2 |
| #21460770 | 2 |
| C2×#16839827 | 2 |
| #11631 | 61 |