Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1328 conjugacy classes of subgroups; only the 291 normal subgroups are shown.
This group has 1328 conjugacy classes of subgroups — too many to draw. Only its 291 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 |
| 2. #21454514 | C2 | semidirect |
| 3. #21446238 | C2 | semidirect |
| 4. #21446107 | C2 | semidirect |
| 5. #21445770 | C2 | semidirect |
| 6. #21445621 | C2 | semidirect |
| 12. C23×#92418 | C22 | semidirect |
| 15. #16839789 | C22 | semidirect |
| 18. #16839726 | C22 | semidirect |
| 19. #16839718 | C22 | semidirect |
| 20. #16839532 | C22 | semidirect |
| 33. C2×#11758194 | D4 | semidirect |
| 39. C22×#92418 | D4 | 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 |
| #21454514 | 2 |
| #21446238 | 2 |
| #21446107 | 2 |
| #21445770 | 2 |
| #21445621 | 2 |
| C61×#3025 | 2 |
| #21483 | 61 |