Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
676 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 676 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. #21446799 | C2 | semidirect |
| 3. #21444547 | C2 | semidirect |
| 4. #21444456 | C2 | semidirect |
| 5. #21444332 | C2 | semidirect |
| 12. #16840482 | C4 | semidirect |
| 14. D4×Dic122 | C4 | semidirect |
| 239. C61 | #8496 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460233 | 2 |
| #21446799 | 2 |
| #21444547 | 2 |
| #21444456 | 2 |
| #21444332 | 2 |
| #21444327 | 2 |
| C61×#1557 | 2 |
| #8496 | 61 |