Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
624 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 170 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. #21462708 | C2 | semidirect |
| 2. #21461440 | C2 | semidirect |
| 3. #21461420 | C2 | semidirect |
| 4. #21461382 | C2 | semidirect |
| 5. #21461179 | C2 | semidirect |
| 6. #21461033 | C2 | semidirect |
| 171. C61 | #17989 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462708 | 2 |
| #21461440 | 2 |
| #21461420 | 2 |
| #21461382 | 2 |
| #21461179 | 2 |
| #21461033 | 2 |
| #21456396 | 2 |
| #17989 | 61 |