Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 400 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. #21444445 | C2 | semidirect |
| 5. #21444174 | C2 | semidirect |
| 6. #21443731 | C2 | semidirect |
| 7. C61×#1287 | C2 | semidirect |
| 153. #1287 | D61 | semidirect |
| 178. C61 | #9335 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457011 | 2 |
| #21454889 | 2 |
| #21444522 | 2 |
| #21444445 | 2 |
| #21444174 | 2 |
| #21443731 | 2 |
| C61×#1287 | 2 |
| #9335 | 61 |