Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1306 conjugacy classes of subgroups; only the 279 normal subgroups are shown.
This group has 1306 conjugacy classes of subgroups — too many to draw. Only its 279 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 |
|---|---|---|
| 2. #21454520 | C2 | semidirect |
| 3. #21446237 | C2 | semidirect |
| 4. #21446105 | C2 | semidirect |
| 5. #21445770 | C2 | semidirect |
| 6. #21445619 | C2 | semidirect |
| 7. C61×#3573 | C2 | semidirect |
| 8. C22×#11758189 | C22 | semidirect |
| 14. #16839790 | C22 | semidirect |
| 18. #16839725 | C22 | semidirect |
| 19. #16839717 | C22 | semidirect |
| 20. #16839533 | C22 | semidirect |
| 57. C2×M16×C61 | D4 | semidirect |
| 60. C22×C8×C61 | D4 | semidirect |
| 141. #3573 | D61 | semidirect |
| 170. C61 | #21484 | semidirect |
| 187. C2×M16 | C22⋊D61 | semidirect |
| 191. C22×C8 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455211 | 2 |
| #21454520 | 2 |
| #21446237 | 2 |
| #21446105 | 2 |
| #21445770 | 2 |
| #21445619 | 2 |
| C61×#3573 | 2 |
| #21484 | 61 |