Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
682 conjugacy classes of subgroups; only the 155 normal subgroups are shown.
This group has 682 conjugacy classes of subgroups — too many to draw. Only its 155 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. #21456332 | C2 | semidirect |
| 3. #21448062 | C2 | semidirect |
| 4. #21448061 | C2 | semidirect |
| 5. #21448060 | C2 | semidirect |
| 6. #21448041 | C2 | semidirect |
| 7. #21447533 | C2 | semidirect |
| 8. #21447412 | C2 | semidirect |
| 9. C61×#2244 | C2 | semidirect |
| 15. #16840166 | C22 | semidirect |
| 16. #16840164 | C22 | semidirect |
| 26. #16839564 | C22 | semidirect |
| 27. #16839563 | C22 | semidirect |
| 28. #16839562 | C22 | semidirect |
| 29. #16839538 | C22 | semidirect |
| 30. C16×Dic61 | C22 | semidirect |
| 31. C61×#499 | C22 | semidirect |
| 33. C61×#357 | C22 | semidirect |
| 34. C61×#346 | C22 | semidirect |
| 156. #2244 | D61 | semidirect |
| 173. #499 | C2×D61 | semidirect |
| 186. #357 | C2×D61 | semidirect |
| 188. #346 | C2×D61 | semidirect |
| 190. C61 | #33704 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456332 | 2 |
| #493×D61 | 2 |
| #21448062 | 2 |
| #21448061 | 2 |
| #21448060 | 2 |
| #21448041 | 2 |
| #21447533 | 2 |
| #21447412 | 2 |
| C61×#2244 | 2 |
| #33704 | 61 |