Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
242 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 122 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. #21460844 | C2 | semidirect |
| 4. #21460843 | C2 | semidirect |
| 34. M32×C61 | C8 | semidirect |
| 54. C16×C61 | C2×C8 | semidirect |
| 108. C61 | #12000 | semidirect |
| 114. M32 | #92420 | semidirect |
| 146. C16 | C2×#92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461366 | 2 |
| C2×#16840623 | 2 |
| #21460844 | 2 |
| #21460843 | 2 |
| M32×Dic61 | 2 |
| #12000 | 61 |