Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 76 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. #21462708 | C2 | semidirect |
| 2. #21461208 | C2 | semidirect |
| 3. #21461208 | C2 | semidirect |
| 4. #21461179 | C2 | semidirect |
| 5. #21460676 | C2 | semidirect |
| 6. #21460642 | C2 | semidirect |
| 22. #16840134 | C4 | semidirect |
| 23. #16840113 | C4 | semidirect |
| 24. #16840108 | C4 | semidirect |
| 28. C61×#493 | C4 | semidirect |
| 188. #493 | #6923 | semidirect |
| 207. C61 | #9281 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462708 | 2 |
| #21461208 | 2 |
| #21461179 | 2 |
| #21460676 | 2 |
| #21460642 | 2 |
| #21456747 | 2 |
| #9281 | 61 |