Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 4. #21444163 | C2 | semidirect |
| 5. #21443731 | C2 | semidirect |
| 6. #21443691 | C2 | semidirect |
| 7. C61×#1491 | C2 | semidirect |
| 193. #1491 | D61 | semidirect |
| 229. C61 | #9531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455990 | 2 |
| #21454804 | 2 |
| #21444451 | 2 |
| #21444163 | 2 |
| #21443731 | 2 |
| #21443691 | 2 |
| C61×#1491 | 2 |
| #9531 | 61 |