Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
400 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 100 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. #21461537 | C2 | semidirect |
| 4. C8×#11758213 | C2 | semidirect |
| 5. #21460712 | C2 | semidirect |
| 6. #21460706 | C2 | semidirect |
| 14. #16840619 | C4 | semidirect |
| 15. #16840618 | C4 | semidirect |
| 21. Q8×#92418 | C4 | semidirect |
| 22. #16839841 | C4 | semidirect |
| 25. #16839827 | C4 | semidirect |
| 30. C61×#446 | C4 | semidirect |
| 178. #446 | #6923 | semidirect |
| 200. C61 | #8250 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461537 | 2 |
| #21461271 | 2 |
| #21461192 | 2 |
| C8×#11758213 | 2 |
| #21460712 | 2 |
| #21460706 | 2 |
| #21454793 | 2 |
| #8250 | 61 |