Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
530 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 99 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. #21446737 | C2 | semidirect |
| 3. #21444417 | C2 | semidirect |
| 4. #21444365 | C2 | semidirect |
| 5. #21443683 | C2 | semidirect |
| 6. #21443675 | C2 | semidirect |
| 7. C61×#2337 | C2 | semidirect |
| 9. #16840152 | C4 | semidirect |
| 10. #16840121 | C4 | semidirect |
| 35. #14519777 | C2×C4 | semidirect |
| 36. #14519774 | C2×C4 | semidirect |
| 52. #14519688 | C2×C4 | semidirect |
| 216. #2337 | D61 | semidirect |
| 252. C61 | #9381 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456806 | 2 |
| #21446737 | 2 |
| #21444417 | 2 |
| #21444365 | 2 |
| #21443683 | 2 |
| #21443675 | 2 |
| C61×#2337 | 2 |
| #9381 | 61 |