Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
778 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 778 conjugacy classes of subgroups — too many to draw. Only its 143 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. #21457631 | C2 | semidirect |
| 2. #21457418 | C2 | semidirect |
| 3. #21445281 | C2 | semidirect |
| 4. #21445253 | C2 | semidirect |
| 5. #21445051 | C2 | semidirect |
| 6. #21444871 | C2 | semidirect |
| 7. #21444705 | C2 | semidirect |
| 8. C8×D488 | C2 | semidirect |
| 9. C61×#1706 | C2 | semidirect |
| 12. #16840397 | C22 | semidirect |
| 14. #16840039 | C22 | semidirect |
| 17. #16839964 | C22 | semidirect |
| 25. #16839841 | C22 | semidirect |
| 26. C8×D244 | C22 | semidirect |
| 28. #16839515 | C22 | semidirect |
| 29. #16839515 | C22 | semidirect |
| 30. #16839508 | C22 | semidirect |
| 31. #16839506 | C22 | semidirect |
| 32. #16839491 | C22 | semidirect |
| 33. #16839491 | C22 | semidirect |
| 34. C61×#500 | C22 | semidirect |
| 36. C61×#492 | C22 | semidirect |
| 37. C61×#486 | C22 | semidirect |
| 38. C82×C61 | C22 | semidirect |
| 126. D488 | D8 | semidirect |
| 189. #1706 | D61 | semidirect |
| 205. #500 | C2×D61 | semidirect |
| 207. #492 | C2×D61 | semidirect |
| 208. #486 | C2×D61 | semidirect |
| 230. C82 | C2×D61 | semidirect |
| 231. C61 | #19884 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21457631 | 2 |
| #21457418 | 2 |
| #21445281 | 2 |
| #21445253 | 2 |
| #21445051 | 2 |
| #21444871 | 2 |
| #21444705 | 2 |
| C8×D488 | 2 |
| C61×#1706 | 2 |
| #19884 | 61 |