Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
424 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 424 conjugacy classes of subgroups — too many to draw. Only its 92 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. #21462171 | C2 | semidirect |
| 4. #21460891 | C2 | semidirect |
| 19. #16839544 | C4 | semidirect |
| 20. #16839543 | C4 | semidirect |
| 21. C61×#349 | C4 | semidirect |
| 50. #14519717 | C2×C4 | semidirect |
| 54. M32×C61 | C2×C4 | semidirect |
| 185. #349 | #6923 | semidirect |
| 187. C61 | #12923 | semidirect |
| 210. M32 | C2×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462472 | 2 |
| #21462171 | 2 |
| #21461697 | 2 |
| #21460891 | 2 |
| #349×D61 | 2 |
| #12923 | 61 |