Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 90 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. #21460807 | C2 | semidirect |
| 15. #16840000 | C4 | semidirect |
| 17. C2×#14519711 | C4 | semidirect |
| 19. C22×Q16×C61 | C4 | semidirect |
| 152. C22×Q16 | #6923 | semidirect |
| 167. C61 | #11706 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462048 | 2 |
| #21461505 | 2 |
| #21460807 | 2 |
| C2×#16840000 | 2 |
| #11706 | 61 |