Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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. #21454430 | C2 | semidirect |
| 2. #21448031 | C2 | semidirect |
| 3. #21447591 | C2 | semidirect |
| 4. C2×#16839575 | C2 | semidirect |
| 5. #21447440 | C2 | semidirect |
| 10. #16839811 | C22 | semidirect |
| 13. #16839584 | C22 | semidirect |
| 15. #16839544 | C22 | semidirect |
| 153. C61 | #33657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454430 | 2 |
| #21448031 | 2 |
| #21447591 | 2 |
| C2×#16839575 | 2 |
| #21447440 | 2 |
| C61×#3058 | 2 |
| #33657 | 61 |