Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
642 conjugacy classes of subgroups; only the 236 normal subgroups are shown.
This group has 642 conjugacy classes of subgroups — too many to draw. Only its 236 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. #21462788 | C2 | semidirect |
| 2. #21462211 | C2 | semidirect |
| 3. #21462208 | C2 | semidirect |
| 4. #21462160 | C2 | semidirect |
| 5. C2×#16840661 | C2 | semidirect |
| 6. #21462030 | C2 | semidirect |
| 9. #16840821 | C22 | semidirect |
| 14. #16840684 | C22 | semidirect |
| 15. #16840661 | C22 | semidirect |
| 16. #16840661 | C22 | semidirect |
| 17. #16840651 | C22 | semidirect |
| 18. #16840648 | C22 | semidirect |
| 147. C61 | #33442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462788 | 2 |
| #21462211 | 2 |
| #21462208 | 2 |
| #21462160 | 2 |
| C2×#16840661 | 2 |
| #21462030 | 2 |
| #21454721 | 2 |
| #33442 | 61 |