Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
384 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 384 conjugacy classes of subgroups — too many to draw. Only its 107 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. C4×#14519709 | C2 | semidirect |
| 4. #21443674 | C2 | semidirect |
| 5. C61×#1568 | C2 | semidirect |
| 7. #16839892 | C4 | semidirect |
| 8. C8×Dic122 | C4 | semidirect |
| 9. #16839841 | C4 | semidirect |
| 11. C8×D244 | C4 | semidirect |
| 150. #1568 | D61 | semidirect |
| 177. C61 | #8696 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454794 | 2 |
| C4×#14519709 | 2 |
| #21444345 | 2 |
| #21443674 | 2 |
| C61×#1568 | 2 |
| #8696 | 61 |