Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
298 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 156 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. #21460736 | C2 | semidirect |
| 4. #21460735 | C2 | semidirect |
| 26. #14519717 | C8 | semidirect |
| 33. M32×C61 | C8 | semidirect |
| 51. C16×C61 | C2×C8 | semidirect |
| 52. #11758185 | C2×C8 | semidirect |
| 97. C61 | #11404 | semidirect |
| 104. M32 | #92420 | semidirect |
| 132. C16 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462025 | 2 |
| C2×#16840603 | 2 |
| #21460736 | 2 |
| #21460735 | 2 |
| M32×Dic61 | 2 |
| #11404 | 61 |