Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
464 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21448098 | C2 | semidirect |
| 3. #21448026 | C2 | semidirect |
| 4. #21448020 | C2 | semidirect |
| 5. #21447983 | C2 | semidirect |
| 6. #21447924 | C2 | semidirect |
| 8. #21447604 | C2 | semidirect |
| 9. C4×Q32×C61 | C2 | semidirect |
| 135. C4×Q32 | D61 | semidirect |
| 167. C61 | #33919 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458189 | 2 |
| #21448098 | 2 |
| #21448026 | 2 |
| #21448020 | 2 |
| #21447983 | 2 |
| #21447924 | 2 |
| #21447652 | 2 |
| #21447604 | 2 |
| C4×Q32×C61 | 2 |
| #33919 | 61 |