Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
498 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 498 conjugacy classes of subgroups — too many to draw. Only its 79 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. #21447484 | C2 | semidirect |
| 2. #21444411 | C2 | semidirect |
| 3. #21443970 | C2 | semidirect |
| 7. #16839557 | C22 | semidirect |
| 10. #16839502 | C22 | semidirect |
| 11. C61×#585 | C4 | semidirect |
| 14. C61×#456 | C4 | semidirect |
| 19. C61×#413 | C4 | semidirect |
| 179. #585 | Dic61 | semidirect |
| 182. #456 | Dic61 | semidirect |
| 187. #413 | Dic61 | semidirect |
| 194. C61 | #13568 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21447484 | 2 |
| #21444411 | 2 |
| #21443970 | 2 |
| C61×#3018 | 2 |
| #13568 | 61 |