Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
456 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 112 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. #21462786 | C2 | semidirect |
| 2. #21462063 | C2 | semidirect |
| 3. C2×#16840660 | C2 | semidirect |
| 4. #21462051 | C2 | semidirect |
| 5. #21460873 | C2 | semidirect |
| 6. #21460869 | 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 |
|---|---|
| #21462786 | 2 |
| #21462063 | 2 |
| C2×#16840660 | 2 |
| #21462051 | 2 |
| #21460873 | 2 |
| #21460869 | 2 |
| #21454718 | 2 |
| #12979 | 61 |