Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
412 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 412 conjugacy classes of subgroups — too many to draw. Only its 82 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 |
|---|---|---|
| 3. #21461397 | C2 | semidirect |
| 4. #21461396 | C2 | semidirect |
| 5. #21460646 | C2 | semidirect |
| 6. #21460646 | C2 | semidirect |
| 25. #16839511 | C4 | semidirect |
| 26. #16839505 | C4 | semidirect |
| 27. #16839505 | C4 | semidirect |
| 28. C61×#333 | C4 | semidirect |
| 188. #333 | #6923 | semidirect |
| 191. C61 | #8934 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462702 | 2 |
| #21461952 | 2 |
| #21461397 | 2 |
| #21461396 | 2 |
| #21460646 | 2 |
| #21444480 | 2 |
| #8934 | 61 |