Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
748 conjugacy classes of subgroups; only the 163 normal subgroups are shown.
This group has 748 conjugacy classes of subgroups — too many to draw. Only its 163 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. C2×#16840197 | C2 | semidirect |
| 2. C22×D976 | C2 | semidirect |
| 3. #21456306 | C2 | semidirect |
| 4. #21454670 | C2 | semidirect |
| 5. #21447877 | C2 | semidirect |
| 6. #21447853 | C2 | semidirect |
| 7. #21447577 | C2 | semidirect |
| 8. #21447534 | C2 | semidirect |
| 9. C61×#2138 | C2 | semidirect |
| 16. C2×#14519720 | C22 | semidirect |
| 19. C2×#14519718 | C22 | semidirect |
| 22. #16840147 | C22 | semidirect |
| 23. #16840137 | C22 | semidirect |
| 25. #16839844 | C22 | semidirect |
| 28. #16839580 | C22 | semidirect |
| 29. #16839562 | C22 | semidirect |
| 33. C61×#358 | C22 | semidirect |
| 34. C61×#357 | C22 | semidirect |
| 44. C2×D488 | D4 | semidirect |
| 184. #2138 | D61 | semidirect |
| 213. #358 | C2×D61 | semidirect |
| 215. #357 | C2×D61 | semidirect |
| 216. C61 | #33585 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840197 | 2 |
| C22×D976 | 2 |
| #21456306 | 2 |
| #21454670 | 2 |
| #21447877 | 2 |
| #21447853 | 2 |
| #21447577 | 2 |
| #21447534 | 2 |
| C61×#2138 | 2 |
| #33585 | 61 |