Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
526 conjugacy classes of subgroups; only the 270 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 270 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. #21462233 | C2 | semidirect |
| 2. Q8×#11758187 | C2 | semidirect |
| 38. Q8×D61 | C16 | semidirect |
| 109. C61 | #33496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462233 | 2 |
| Q8×#11758187 | 2 |
| #21462179 | 2 |
| #21462178 | 2 |
| C8×Q8×D61 | 2 |
| #33496 | 61 |