Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
444 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 102 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 |
|---|---|---|
| 2. #21461476 | C2 | semidirect |
| 4. #21461020 | C2 | semidirect |
| 5. #21460714 | C2 | semidirect |
| 6. #21460707 | C2 | semidirect |
| 8. #16840812 | C4 | semidirect |
| 9. #16840811 | C4 | semidirect |
| 10. #16840797 | C4 | semidirect |
| 13. D4×#92420 | C4 | semidirect |
| 22. #16840619 | C4 | semidirect |
| 23. #16840617 | C4 | semidirect |
| 220. C61 | #8247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462632 | 2 |
| #21461476 | 2 |
| #21461270 | 2 |
| #21461020 | 2 |
| #21460714 | 2 |
| #21460707 | 2 |
| #21444302 | 2 |
| #8247 | 61 |