Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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. #14558014 | C2 | semidirect |
| 3. #14557856 | C2 | semidirect |
| 4. #14557855 | C2 | semidirect |
| 5. #14557850 | C2 | semidirect |
| 6. #14557845 | C2 | semidirect |
| 7. #14557573 | C2 | semidirect |
| 8. #14557571 | C2 | semidirect |
| 9. #14557538 | C2 | semidirect |
| 10. #14557499 | C2 | semidirect |
| 11. C2×#102×C37 | C2 | semidirect |
| 24. #11924494 | C22 | semidirect |
| 25. C4⋊C4×D37 | C22 | semidirect |
| 26. #11924470 | C22 | semidirect |
| 27. #11924470 | C22 | semidirect |
| 28. #11924469 | C22 | semidirect |
| 29. #11924468 | C22 | semidirect |
| 30. #11924468 | C22 | semidirect |
| 31. #11924467 | C22 | semidirect |
| 34. #11924448 | C22 | semidirect |
| 35. #11924448 | C22 | semidirect |
| 144. C2×#102 | D37 | semidirect |
| 146. C37 | #3096 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558100 | 2 |
| #14558014 | 2 |
| #14557856 | 2 |
| #14557855 | 2 |
| #14557850 | 2 |
| #14557845 | 2 |
| #14557573 | 2 |
| #14557571 | 2 |
| #14557538 | 2 |
| #14557499 | 2 |
| C2×#102×C37 | 2 |
| #3096 | 37 |