Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
354 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 354 conjugacy classes of subgroups — too many to draw. Only its 74 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. D61⋊#365 | C2 | semidirect |
| 4. #21461640 | C2 | semidirect |
| 5. #21460885 | C2 | semidirect |
| 6. #21460865 | C2 | semidirect |
| 23. #16839576 | C4 | semidirect |
| 24. #16839575 | C4 | semidirect |
| 25. #16839574 | C4 | semidirect |
| 26. C61×#361 | C4 | semidirect |
| 184. #361 | #6923 | semidirect |
| 186. C61 | #13138 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D61⋊#365 | 2 |
| D61⋊#361 | 2 |
| #21461968 | 2 |
| #21461640 | 2 |
| #21460885 | 2 |
| #21460865 | 2 |
| #361×D61 | 2 |
| #13138 | 61 |