Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
442 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 442 conjugacy classes of subgroups — too many to draw. Only its 97 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. #21447568 | C2 | semidirect |
| 2. #21447555 | C2 | semidirect |
| 3. #21446572 | C2 | semidirect |
| 4. #21443899 | C2 | semidirect |
| 27. #14519709 | D4 | semidirect |
| 152. C61 | #13416 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447568 | 2 |
| #21447555 | 2 |
| #21446572 | 2 |
| #21443899 | 2 |
| C61×#3150 | 2 |
| #13416 | 61 |