Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462161 | C2 | semidirect |
| 4. #21461739 | C2 | semidirect |
| 5. #21460901 | C2 | semidirect |
| 6. #21460886 | C2 | semidirect |
| 20. #16839875 | C4 | semidirect |
| 21. #16839874 | C4 | semidirect |
| 22. #16839873 | C4 | semidirect |
| 28. C61×#442 | C4 | semidirect |
| 198. #442 | #6923 | semidirect |
| 212. C61 | #12826 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462161 | 2 |
| D61⋊#361 | 2 |
| #21462128 | 2 |
| #21461739 | 2 |
| #21460901 | 2 |
| #21460886 | 2 |
| #21454668 | 2 |
| #12826 | 61 |