Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
612 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 178 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. #21461921 | C2 | semidirect |
| 3. #21461879 | C2 | semidirect |
| 5. #21461753 | C2 | semidirect |
| 6. #21461748 | C2 | semidirect |
| 140. C61 | #23380 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21461921 | 2 |
| #21461893 | 2 |
| #21461879 | 2 |
| #21461763 | 2 |
| #21461753 | 2 |
| #21461748 | 2 |
| #21449121 | 2 |
| #23380 | 61 |