Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
382 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 116 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 |
|---|---|---|
| 3. #21462042 | C2 | semidirect |
| 4. C2×#16840655 | C2 | semidirect |
| 5. #21460870 | C2 | semidirect |
| 6. #21460867 | C2 | semidirect |
| 9. #16840821 | C4 | semidirect |
| 15. #16840661 | C4 | semidirect |
| 167. C61 | #12618 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462788 | 2 |
| #21462063 | 2 |
| #21462042 | 2 |
| C2×#16840655 | 2 |
| #21460870 | 2 |
| #21460867 | 2 |
| #21445662 | 2 |
| #12618 | 61 |