Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
416 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 416 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. #21462724 | C2 | semidirect |
| 2. #21461211 | C2 | semidirect |
| 5. #21460676 | C2 | semidirect |
| 6. #21460642 | C2 | semidirect |
| 22. #16840142 | C4 | semidirect |
| 23. #16840134 | C4 | semidirect |
| 24. #16840114 | C4 | semidirect |
| 28. C61×#486 | C4 | semidirect |
| 180. #486 | #6923 | semidirect |
| 196. C61 | #9282 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462724 | 2 |
| #21461211 | 2 |
| #21461208 | 2 |
| #21461179 | 2 |
| #21460676 | 2 |
| #21460642 | 2 |
| #21456776 | 2 |
| #9282 | 61 |