Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
708 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 708 conjugacy classes of subgroups — too many to draw. Only its 124 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. #21461675 | C2 | semidirect |
| 2. C2×#16840628 | C2 | semidirect |
| 3. #21460636 | C2 | semidirect |
| 4. #21460635 | C2 | semidirect |
| 258. C61 | #7664 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461675 | 2 |
| C2×#16840628 | 2 |
| #21460636 | 2 |
| #21460635 | 2 |
| #21454162 | 2 |
| #7664 | 61 |