Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
712 conjugacy classes of subgroups; only the 171 normal subgroups are shown.
This group has 712 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×#16840203 | C2 | semidirect |
| 3. #21454687 | C2 | semidirect |
| 4. #21447879 | C2 | semidirect |
| 5. #21447857 | C2 | semidirect |
| 6. #21447577 | C2 | semidirect |
| 7. #21447535 | C2 | semidirect |
| 8. #21447527 | C2 | semidirect |
| 9. C22×SD32×C61 | C2 | semidirect |
| 15. C2×#14519723 | C22 | semidirect |
| 16. C2×#14519720 | C22 | semidirect |
| 22. Q16×Dic61 | C22 | semidirect |
| 26. #16839580 | C22 | semidirect |
| 27. #16839567 | C22 | semidirect |
| 28. #16839564 | C22 | semidirect |
| 67. C2×Q16×C61 | D4 | semidirect |
| 173. C22×SD32 | D61 | semidirect |
| 211. C61 | #33587 | semidirect |
| 221. C2×Q16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840203 | 2 |
| #21456300 | 2 |
| #21454687 | 2 |
| #21447879 | 2 |
| #21447857 | 2 |
| #21447577 | 2 |
| #21447535 | 2 |
| #21447527 | 2 |
| C22×SD32×C61 | 2 |
| #33587 | 61 |