Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
488 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 127 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. #21456451 | C2 | semidirect |
| 2. #21447970 | C2 | semidirect |
| 3. #21447954 | C2 | semidirect |
| 4. #21447930 | C2 | semidirect |
| 5. #21447910 | C2 | semidirect |
| 6. #21447880 | C2 | semidirect |
| 7. #21447872 | C2 | semidirect |
| 8. #21447577 | C2 | semidirect |
| 180. C61 | #33828 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456451 | 2 |
| #21447970 | 2 |
| #21447954 | 2 |
| #21447930 | 2 |
| #21447910 | 2 |
| #21447880 | 2 |
| #21447872 | 2 |
| #21447577 | 2 |
| C61×#2215 | 2 |
| #33828 | 61 |