Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
872 conjugacy classes of subgroups; only the 224 normal subgroups are shown.
This group has 872 conjugacy classes of subgroups — too many to draw. Only its 224 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. #21461310 | C2 | semidirect |
| 4. #21461283 | C2 | semidirect |
| 5. #21461281 | C2 | semidirect |
| 6. #21461276 | C2 | semidirect |
| 193. C61 | #17692 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462665 | 2 |
| #21461310 | 2 |
| #21461283 | 2 |
| #21461281 | 2 |
| #21461276 | 2 |
| #21459641 | 2 |
| #17692 | 61 |