Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
428 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 428 conjugacy classes of subgroups — too many to draw. Only its 108 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 |
|---|---|---|
| 3. M32×#6923 | C2 | semidirect |
| 4. #21461624 | C2 | semidirect |
| 5. #21460900 | C2 | semidirect |
| 6. #21460898 | C2 | semidirect |
| 12. #16840804 | C4 | semidirect |
| 13. #16840804 | C4 | semidirect |
| 19. #16840678 | C4 | semidirect |
| 26. #16839579 | C4 | semidirect |
| 27. #16839577 | C4 | semidirect |
| 28. #16839575 | C4 | semidirect |
| 29. C61×#361 | C4 | semidirect |
| 196. #361 | #6923 | semidirect |
| 201. C61 | #12646 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840804 | 2 |
| #21462140 | 2 |
| M32×#6923 | 2 |
| #21461624 | 2 |
| #21460900 | 2 |
| #21460898 | 2 |
| #21447565 | 2 |
| #12646 | 61 |