Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 558 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. #21462743 | C2 | semidirect |
| 2. #21461986 | C2 | semidirect |
| 3. #21461694 | C2 | semidirect |
| 4. #21461327 | C2 | semidirect |
| 5. #21460715 | C2 | semidirect |
| 6. #21460688 | C2 | semidirect |
| 25. #16839962 | C4 | semidirect |
| 27. #16839958 | C4 | semidirect |
| 29. #16839954 | C4 | semidirect |
| 32. C61×#460 | C4 | semidirect |
| 257. #460 | #6923 | semidirect |
| 277. C61 | #9322 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462743 | 2 |
| #21461986 | 2 |
| #21461694 | 2 |
| #21461327 | 2 |
| #21460715 | 2 |
| #21460688 | 2 |
| #21455296 | 2 |
| #9322 | 61 |