Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
300 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462160 | C2 | semidirect |
| 4. C2×#16840654 | C2 | semidirect |
| 5. #21460870 | C2 | semidirect |
| 6. #21460866 | C2 | semidirect |
| 161. C61 | #13127 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462160 | 2 |
| #21462061 | 2 |
| #21462055 | 2 |
| C2×#16840654 | 2 |
| #21460870 | 2 |
| #21460866 | 2 |
| #21445664 | 2 |
| #13127 | 61 |