Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
540 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 540 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 |
|---|---|---|
| 1. #21462746 | C2 | semidirect |
| 2. #21461961 | C2 | semidirect |
| 3. #21461326 | C2 | semidirect |
| 4. #21461156 | C2 | semidirect |
| 5. #21460727 | C2 | semidirect |
| 6. #21460703 | C2 | semidirect |
| 184. D244 | #100 | semidirect |
| 266. C61 | #9359 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21462746 | 2 |
| #21461961 | 2 |
| #21461326 | 2 |
| #21461156 | 2 |
| #21460727 | 2 |
| #21460703 | 2 |
| #21455298 | 2 |
| #9359 | 61 |