Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
308 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 308 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 14. #16840687 | C4 | semidirect |
| 15. #16840686 | C4 | semidirect |
| 16. #16840649 | C4 | semidirect |
| 17. C16×#6923 | C4 | semidirect |
| 23. #16839586 | C4 | semidirect |
| 24. #16839585 | C4 | semidirect |
| 25. #16839584 | C4 | semidirect |
| 26. C61×#365 | C4 | semidirect |
| 160. #365 | #6923 | semidirect |
| 165. C61 | #12668 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462167 | 2 |
| M32×#6923 | 2 |
| #21461624 | 2 |
| #21461622 | 2 |
| #21460888 | 2 |
| #21460886 | 2 |
| #21447590 | 2 |
| #12668 | 61 |