Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
390 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 390 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. #21462161 | C2 | semidirect |
| 4. #21461739 | C2 | semidirect |
| 5. #21460892 | C2 | semidirect |
| 6. #21460883 | C2 | semidirect |
| 20. #16839875 | C4 | semidirect |
| 21. #16839873 | C4 | semidirect |
| 22. #16839869 | C4 | semidirect |
| 28. C61×#441 | C4 | semidirect |
| 190. #441 | #6923 | semidirect |
| 204. C61 | #12828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462161 | 2 |
| #21462141 | 2 |
| #21462135 | 2 |
| #21461739 | 2 |
| #21460892 | 2 |
| #21460883 | 2 |
| #21454699 | 2 |
| #12828 | 61 |