Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
686 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 159 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. #499×D61 | C2 | semidirect |
| 3. #21448062 | C2 | semidirect |
| 4. #21448061 | C2 | semidirect |
| 5. #21448060 | C2 | semidirect |
| 6. #21448059 | C2 | semidirect |
| 7. #357×D61 | C2 | semidirect |
| 8. #346×D61 | C2 | semidirect |
| 9. C61×#2244 | C2 | semidirect |
| 15. #16840164 | C22 | semidirect |
| 16. #16840163 | C22 | semidirect |
| 26. #16839564 | C22 | semidirect |
| 27. #16839563 | C22 | semidirect |
| 28. #16839562 | C22 | semidirect |
| 29. #16839538 | C22 | semidirect |
| 30. #16839537 | C22 | semidirect |
| 31. C61×#499 | C22 | semidirect |
| 33. C61×#357 | C22 | semidirect |
| 34. C61×#346 | C22 | semidirect |
| 157. #2244 | D61 | direct (N × H) |
| 164. D61 | #2244 | direct (N × H) |
| 174. #499 | C2×D61 | semidirect |
| 186. #357 | C2×D61 | semidirect |
| 189. #346 | C2×D61 | semidirect |
| 190. C61 | C2×#2244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×D61 | 2 |
| #493×D61 | 2 |
| #21448062 | 2 |
| #21448061 | 2 |
| #21448060 | 2 |
| #21448059 | 2 |
| #357×D61 | 2 |
| #346×D61 | 2 |
| C61×#2244 | 2 |
| C2×#2244 | 61 |