Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 98 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. #21461538 | C2 | semidirect |
| 4. #21461020 | C2 | semidirect |
| 5. #21460714 | C2 | semidirect |
| 6. #21460707 | C2 | semidirect |
| 8. #16840813 | C4 | semidirect |
| 9. Q8×#92420 | C4 | semidirect |
| 10. #16840796 | C4 | semidirect |
| 12. #16840790 | C4 | semidirect |
| 22. #16840619 | C4 | semidirect |
| 23. #16840618 | C4 | semidirect |
| 218. C61 | #8250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462635 | 2 |
| #21461538 | 2 |
| #21461272 | 2 |
| #21461020 | 2 |
| #21460714 | 2 |
| #21460707 | 2 |
| #21444304 | 2 |
| #8250 | 61 |