Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
338 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 74 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. #21461745 | C2 | semidirect |
| 3. #21461385 | C2 | semidirect |
| 5. #21460713 | C2 | semidirect |
| 6. #21460704 | C2 | semidirect |
| 196. C61 | #8917 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462777 | 2 |
| #21461745 | 2 |
| #21461385 | 2 |
| #21461177 | 2 |
| #21460713 | 2 |
| #21460704 | 2 |
| #21444406 | 2 |
| #8917 | 61 |