Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
766 conjugacy classes of subgroups; only the 111 normal subgroups are shown.
This group has 766 conjugacy classes of subgroups — too many to draw. Only its 111 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 |
|---|---|---|
| 2. #21446618 | C2 | semidirect |
| 3. #21444520 | C2 | semidirect |
| 4. #21444515 | C2 | semidirect |
| 5. #21444435 | C2 | semidirect |
| 6. #21444431 | C2 | semidirect |
| 7. C61×#1466 | C2 | semidirect |
| 223. #1466 | D61 | semidirect |
| 255. C61 | #8458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21459671 | 2 |
| #21446618 | 2 |
| #21444520 | 2 |
| #21444515 | 2 |
| #21444435 | 2 |
| #21444431 | 2 |
| C61×#1466 | 2 |
| #8458 | 61 |