Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
594 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 594 conjugacy classes of subgroups — too many to draw. Only its 113 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 |
|---|---|---|
| 3. #21446799 | C2 | semidirect |
| 4. #21444384 | C2 | semidirect |
| 5. #21443679 | C2 | semidirect |
| 6. #21443647 | C2 | semidirect |
| 10. #16840134 | C4 | semidirect |
| 11. #16840108 | C4 | semidirect |
| 29. #14519777 | C2×C4 | semidirect |
| 30. #14519777 | C2×C4 | semidirect |
| 48. C4×#92418 | C2×C4 | semidirect |
| 116. C4×Dic61 | SD16 | semidirect |
| 221. C61 | #9295 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456760 | 2 |
| #21448545 | 2 |
| #21446799 | 2 |
| #21444384 | 2 |
| #21443679 | 2 |
| #21443647 | 2 |
| C61×#1545 | 2 |
| #9295 | 61 |