Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
204 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 204 conjugacy classes of subgroups — too many to draw. Only its 66 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. #21462211 | C2 | semidirect |
| 2. #21462209 | C2 | semidirect |
| 3. #21460847 | C2 | semidirect |
| 4. #21460784 | C2 | semidirect |
| 5. #21460783 | C2 | semidirect |
| 6. #21460735 | C2 | semidirect |
| 35. #14519723 | C8 | semidirect |
| 36. #14519721 | C8 | semidirect |
| 37. #14519720 | C8 | semidirect |
| 38. #14519718 | C8 | semidirect |
| 124. C61 | #12068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462211 | 2 |
| #21462209 | 2 |
| #21460847 | 2 |
| #21460784 | 2 |
| #21460783 | 2 |
| #21460735 | 2 |
| #21447702 | 2 |
| #12068 | 61 |