Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1328 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 251 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. #21460531 | C2 | semidirect |
| 3. #21454516 | C2 | semidirect |
| 4. #21446235 | C2 | semidirect |
| 5. #21446104 | C2 | semidirect |
| 6. #21445622 | C2 | semidirect |
| 7. C61×#1791 | C2 | semidirect |
| 12. C22×C8×D61 | C22 | semidirect |
| 18. #16839788 | C22 | semidirect |
| 20. #16839725 | C22 | semidirect |
| 21. #16839720 | C22 | semidirect |
| 22. #16839534 | C22 | semidirect |
| 34. C2×#11758194 | D4 | semidirect |
| 37. C22×#92418 | D4 | semidirect |
| 146. #1791 | D61 | semidirect |
| 170. C61 | #21483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460531 | 2 |
| #21455211 | 2 |
| #21454516 | 2 |
| #21446235 | 2 |
| #21446104 | 2 |
| #21445622 | 2 |
| C61×#1791 | 2 |
| #21483 | 61 |