Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
512 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21448036 | C2 | semidirect |
| 3. #21447992 | C2 | semidirect |
| 4. #21447897 | C2 | semidirect |
| 6. #21447708 | C2 | semidirect |
| 7. #21447635 | C2 | semidirect |
| 8. C61×#3177 | C2 | semidirect |
| 18. #16839584 | C22 | semidirect |
| 19. #16839583 | C22 | semidirect |
| 20. #16839578 | C22 | semidirect |
| 23. #16839540 | C22 | semidirect |
| 25. C61×#499 | C22 | semidirect |
| 26. C61×#494 | C22 | semidirect |
| 30. C61×#441 | C22 | semidirect |
| 157. #3177 | D61 | semidirect |
| 173. #499 | C2×D61 | semidirect |
| 174. #494 | C2×D61 | semidirect |
| 182. #441 | C2×D61 | semidirect |
| 193. C61 | #33693 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21454723 | 2 |
| #21448036 | 2 |
| #21447992 | 2 |
| #21447897 | 2 |
| #21447769 | 2 |
| #21447708 | 2 |
| #21447635 | 2 |
| C61×#3177 | 2 |
| #33693 | 61 |