Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1630 conjugacy classes of subgroups; only the 352 normal subgroups are shown.
This group has 1630 conjugacy classes of subgroups — too many to draw. Only its 352 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 |
|---|---|---|
| 3. #21460999 | C2 | semidirect |
| 8. #16840704 | C4 | semidirect |
| 14. #16839625 | C4 | semidirect |
| 15. #16839624 | C4 | semidirect |
| 16. #16839623 | C4 | semidirect |
| 18. C61×#381 | C4 | semidirect |
| 60. C22×C4×C61 | C42 | semidirect |
| 64. C22×Dic61 | C42 | semidirect |
| 74. C2×C4×D61 | C42 | semidirect |
| 167. #381 | #6923 | semidirect |
| 173. C61 | #13828 | semidirect |
| 229. C22×C4 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840704 | 2 |
| #21461000 | 2 |
| #21460999 | 2 |
| #381×D61 | 2 |
| #13828 | 61 |