Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
632 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 632 conjugacy classes of subgroups — too many to draw. Only its 103 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. #21449000 | C2 | semidirect |
| 2. C2×#16839561 | C2 | semidirect |
| 4. #21443945 | C2 | semidirect |
| 19. C61×#456 | C4 | semidirect |
| 184. #456 | Dic61 | semidirect |
| 196. C61 | #13056 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21449000 | 2 |
| C2×#16839561 | 2 |
| #21445778 | 2 |
| #21443945 | 2 |
| C2×C61×#456 | 2 |
| #13056 | 61 |