Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1122 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 1122 conjugacy classes of subgroups — too many to draw. Only its 183 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. #21460593 | C2 | semidirect |
| 2. C2×#16840198 | C2 | semidirect |
| 3. #21447764 | C2 | semidirect |
| 4. #21447554 | C2 | semidirect |
| 5. #21447440 | C2 | semidirect |
| 6. C61×#3058 | C2 | semidirect |
| 12. #16840562 | C22 | semidirect |
| 16. #16840198 | C22 | semidirect |
| 19. C2×#14519717 | C22 | semidirect |
| 20. #16839571 | C22 | semidirect |
| 21. #16839544 | C22 | semidirect |
| 22. C22×D8×C61 | C22 | semidirect |
| 25. C61×#469 | C22 | semidirect |
| 27. C61×#427 | C22 | semidirect |
| 46. #14519799 | D4 | semidirect |
| 49. C2×Dic244 | D4 | semidirect |
| 53. C2×D488 | D4 | semidirect |
| 199. #3058 | D61 | semidirect |
| 217. C22×D8 | C2×D61 | semidirect |
| 225. #469 | C2×D61 | semidirect |
| 227. #427 | C2×D61 | semidirect |
| 231. C61 | #33531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21460593 | 2 |
| C2×#16840198 | 2 |
| #21447764 | 2 |
| #21447554 | 2 |
| #21447440 | 2 |
| C61×#3058 | 2 |
| #33531 | 61 |