Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
716 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 716 conjugacy classes of subgroups — too many to draw. Only its 171 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. #21456308 | C2 | semidirect |
| 3. #21454671 | C2 | semidirect |
| 4. #21447876 | C2 | semidirect |
| 5. #21447862 | C2 | semidirect |
| 6. #21447577 | C2 | semidirect |
| 7. #21447539 | C2 | semidirect |
| 8. #21447527 | C2 | semidirect |
| 9. C22×SD32×C61 | C2 | semidirect |
| 19. #16840147 | C22 | semidirect |
| 20. #16840140 | C22 | semidirect |
| 26. #16839580 | C22 | semidirect |
| 27. #16839567 | C22 | semidirect |
| 28. #16839566 | C22 | semidirect |
| 29. #16839564 | C22 | semidirect |
| 173. C22×SD32 | D61 | semidirect |
| 211. C61 | #33586 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840198 | 2 |
| #21456308 | 2 |
| #21454671 | 2 |
| #21447876 | 2 |
| #21447862 | 2 |
| #21447577 | 2 |
| #21447539 | 2 |
| #21447527 | 2 |
| C22×SD32×C61 | 2 |
| #33586 | 61 |