Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
954 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 954 conjugacy classes of subgroups — too many to draw. Only its 179 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. #21457202 | C2 | semidirect |
| 3. #21444959 | C2 | semidirect |
| 4. #21444940 | C2 | semidirect |
| 5. #21444897 | C2 | semidirect |
| 6. #21444878 | C2 | semidirect |
| 7. #21444554 | C2 | semidirect |
| 8. #21444274 | C2 | semidirect |
| 9. C61×#3550 | C2 | semidirect |
| 186. #3550 | D61 | semidirect |
| 227. C61 | #18688 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457202 | 2 |
| #21456245 | 2 |
| #21444959 | 2 |
| #21444940 | 2 |
| #21444897 | 2 |
| #21444878 | 2 |
| #21444554 | 2 |
| #21444274 | 2 |
| C61×#3550 | 2 |
| #18688 | 61 |