Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
382 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 3. #21462040 | C2 | semidirect |
| 4. C2×#16840655 | C2 | semidirect |
| 5. #21460869 | C2 | semidirect |
| 6. #21460867 | C2 | semidirect |
| 9. #16840820 | C4 | semidirect |
| 15. #16840660 | 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 |
|---|---|
| #21462786 | 2 |
| #21462061 | 2 |
| #21462040 | 2 |
| C2×#16840655 | 2 |
| #21460869 | 2 |
| #21460867 | 2 |
| #21445666 | 2 |
| #12618 | 61 |