Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1162 conjugacy classes of subgroups; only the 384 normal subgroups are shown.
This group has 1162 conjugacy classes of subgroups — too many to draw. Only its 384 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 |
|---|---|---|
| 1. #21462712 | C2 | semidirect |
| 2. #21461062 | C2 | semidirect |
| 37. C22×Q8×C61 | C8 | semidirect |
| 131. C61 | #17352 | semidirect |
| 134. C22×Q8 | #92420 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462712 | 2 |
| #21461062 | 2 |
| #21461050 | 2 |
| C2×#16840240 | 2 |
| #17352 | 61 |