Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
478 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 86 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. #21462004 | C2 | semidirect |
| 4. #21461142 | C2 | semidirect |
| 5. #21460705 | C2 | semidirect |
| 6. #21460646 | C2 | semidirect |
| 25. #16840044 | C4 | semidirect |
| 26. #16839973 | C4 | semidirect |
| 27. #16839967 | C4 | semidirect |
| 32. C61×#474 | C4 | semidirect |
| 217. #474 | #6923 | semidirect |
| 238. C61 | #8971 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462747 | 2 |
| #21462004 | 2 |
| C4×#14519841 | 2 |
| #21461142 | 2 |
| #21460705 | 2 |
| #21460646 | 2 |
| #21455892 | 2 |
| #8971 | 61 |