Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
588 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 588 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21450848 | C2 | semidirect |
| 3. #21443702 | C2 | semidirect |
| 4. #21443659 | C2 | semidirect |
| 36. #127×C61 | Q8 | semidirect |
| 154. C61 | #10348 | semidirect |
| 164. #127 | Dic122 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21450848 | 2 |
| #21446747 | 2 |
| #21443702 | 2 |
| #21443659 | 2 |
| C61×#1957 | 2 |
| #10348 | 61 |