Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
820 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 820 conjugacy classes of subgroups — too many to draw. Only its 107 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. #21446652 | C2 | semidirect |
| 3. #21444542 | C2 | semidirect |
| 4. #21444328 | C2 | semidirect |
| 5. C61×#1536 | C2 | semidirect |
| 7. #16840478 | C4 | semidirect |
| 10. #16840397 | C4 | semidirect |
| 14. #16839786 | C22 | semidirect |
| 16. #16839608 | C22 | semidirect |
| 21. C61×#432 | C22 | semidirect |
| 153. #1536 | D61 | semidirect |
| 169. #432 | C2×D61 | semidirect |
| 177. C61 | #8491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460224 | 2 |
| #21446652 | 2 |
| #21444542 | 2 |
| #21444328 | 2 |
| C61×#1536 | 2 |
| #8491 | 61 |