Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
636 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 636 conjugacy classes of subgroups — too many to draw. Only its 135 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. #21458968 | C2 | semidirect |
| 2. #21457623 | C2 | semidirect |
| 3. #21447941 | C2 | semidirect |
| 4. #21447897 | C2 | semidirect |
| 5. #21447796 | C2 | semidirect |
| 6. #21447701 | C2 | semidirect |
| 7. #21447657 | C2 | semidirect |
| 8. C61×#2247 | C2 | semidirect |
| 137. #2247 | D61 | semidirect |
| 169. C61 | #33860 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458968 | 2 |
| #21457623 | 2 |
| #21447941 | 2 |
| #21447897 | 2 |
| #21447796 | 2 |
| #21447701 | 2 |
| #21447657 | 2 |
| C61×#2247 | 2 |
| #33860 | 61 |