Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
822 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21448884 | C2 | semidirect |
| 2. #21446747 | C2 | semidirect |
| 3. C2×#16839506 | C2 | semidirect |
| 4. #21443659 | C2 | semidirect |
| 18. C61×#493 | C4 | semidirect |
| 46. #127×C61 | C2×C4 | semidirect |
| 50. C4×C8×C61 | C2×C4 | semidirect |
| 91. C4⋊Dic61 | D8 | semidirect |
| 180. #493 | Dic61 | semidirect |
| 189. C61 | #9061 | semidirect |
| 204. #127 | C2×Dic61 | semidirect |
| 219. C4×C8 | C2×Dic61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21448884 | 2 |
| #21446747 | 2 |
| C2×#16839506 | 2 |
| #21443659 | 2 |
| C2×C61×#493 | 2 |
| #9061 | 61 |