Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 180 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 180 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. #21460730 | C2 | semidirect |
| 4. C16×#92420 | C2 | semidirect |
| 19. #14519852 | C8 | semidirect |
| 27. #14519716 | C8 | semidirect |
| 48. #11758187 | C2×C8 | semidirect |
| 49. C16×C61 | C2×C8 | semidirect |
| 50. #11758185 | C2×C8 | semidirect |
| 60. #92420 | M32 | semidirect |
| 94. C61 | C8×M32 | semidirect |
| 127. C16 | D61⋊C8 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462026 | 2 |
| C8×D61⋊C8 | 2 |
| #21460730 | 2 |
| C16×#92420 | 2 |
| #21447412 | 2 |
| C8×M32 | 61 |