Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 106 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. #21462788 | C2 | semidirect |
| 2. #21462063 | C2 | semidirect |
| 3. C2×#16840661 | C2 | semidirect |
| 4. #21462051 | C2 | semidirect |
| 5. #21460874 | C2 | semidirect |
| 6. #21460870 | C2 | semidirect |
| 204. C61 | #12979 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462788 | 2 |
| #21462063 | 2 |
| C2×#16840661 | 2 |
| #21462051 | 2 |
| #21460874 | 2 |
| #21460870 | 2 |
| #21454721 | 2 |
| #12979 | 61 |