Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
748 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 748 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 |
|---|---|---|
| 1. C2×#16840198 | C2 | semidirect |
| 2. #21456300 | C2 | semidirect |
| 3. #21454671 | C2 | semidirect |
| 4. #21447872 | C2 | semidirect |
| 5. #21447852 | C2 | semidirect |
| 6. #21447577 | C2 | semidirect |
| 7. #21447535 | C2 | semidirect |
| 8. #21447527 | C2 | semidirect |
| 9. C22×D16×C61 | C2 | semidirect |
| 15. C2×#14519721 | C22 | semidirect |
| 16. C2×#14519718 | C22 | semidirect |
| 19. #16840145 | C22 | semidirect |
| 20. #16840137 | C22 | semidirect |
| 22. D8×Dic61 | C22 | semidirect |
| 26. #16839580 | C22 | semidirect |
| 27. #16839567 | C22 | semidirect |
| 28. #16839564 | C22 | semidirect |
| 29. #16839563 | C22 | semidirect |
| 70. C2×D8×C61 | D4 | semidirect |
| 177. C22×D16 | D61 | semidirect |
| 216. C61 | #33585 | semidirect |
| 233. C2×D8 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840198 | 2 |
| #21456300 | 2 |
| #21454671 | 2 |
| #21447872 | 2 |
| #21447852 | 2 |
| #21447577 | 2 |
| #21447535 | 2 |
| #21447527 | 2 |
| C22×D16×C61 | 2 |
| #33585 | 61 |