Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
452 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 452 conjugacy classes of subgroups — too many to draw. Only its 87 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. #21447493 | C2 | semidirect |
| 3. #21447472 | C2 | semidirect |
| 5. #21445863 | C2 | semidirect |
| 6. #21445621 | C2 | semidirect |
| 8. C22×#11758200 | C4 | semidirect |
| 16. #16839798 | C4 | semidirect |
| 17. #16839770 | C4 | semidirect |
| 18. #16839767 | C4 | semidirect |
| 243. C61 | #13229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455455 | 2 |
| #21447493 | 2 |
| #21447472 | 2 |
| #21447469 | 2 |
| #21445863 | 2 |
| #21445621 | 2 |
| C61×#2128 | 2 |
| #13229 | 61 |