Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
466 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 118 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. #21462026 | C2 | semidirect |
| 3. C4×#14519845 | C2 | semidirect |
| 4. #21460890 | C2 | semidirect |
| 9. #16840679 | C4 | semidirect |
| 15. Q16×Dic61 | C4 | semidirect |
| 18. C4×D488 | C4 | semidirect |
| 19. #16839844 | C4 | semidirect |
| 23. C4×Q16×C61 | C4 | semidirect |
| 27. #14519852 | C2×C4 | semidirect |
| 30. #14519845 | C2×C4 | semidirect |
| 77. Q16×C61 | C42 | semidirect |
| 98. D488 | C42 | semidirect |
| 151. Dic61 | #360 | semidirect |
| 167. C4×Q16 | #6923 | semidirect |
| 181. C61 | C4×#360 | semidirect |
| 232. Q16 | C4×#6923 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840679 | 2 |
| #21462026 | 2 |
| C4×#14519845 | 2 |
| #21460890 | 2 |
| C4×#14519800 | 2 |
| C4×#360 | 61 |