Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
712 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 163 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×#16840205 | C2 | semidirect |
| 2. C22×#14519721 | C2 | semidirect |
| 4. #21454686 | C2 | semidirect |
| 5. #21447880 | C2 | semidirect |
| 6. #21447858 | C2 | semidirect |
| 7. #21447579 | C2 | semidirect |
| 8. #21447524 | C2 | semidirect |
| 9. C61×#2140 | C2 | semidirect |
| 16. C2×Dic488 | C22 | semidirect |
| 17. C2×#14519722 | C22 | semidirect |
| 25. #16839856 | C22 | semidirect |
| 28. #16839580 | C22 | semidirect |
| 29. #16839565 | C22 | semidirect |
| 30. #16839562 | C22 | semidirect |
| 42. C2×Dic244 | D4 | semidirect |
| 179. #2140 | D61 | semidirect |
| 211. C61 | #33587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840205 | 2 |
| C22×#14519721 | 2 |
| #21456300 | 2 |
| #21454686 | 2 |
| #21447880 | 2 |
| #21447858 | 2 |
| #21447579 | 2 |
| #21447524 | 2 |
| C61×#2140 | 2 |
| #33587 | 61 |