Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #14558333 | C2 | semidirect |
| 2. C2×#11924562 | C2 | semidirect |
| 3. C2×#11924562 | C2 | semidirect |
| 4. #14558299 | C2 | semidirect |
| 5. #14557802 | C2 | semidirect |
| 6. #14557795 | C2 | semidirect |
| 7. #14557581 | C2 | semidirect |
| 8. #14557515 | C2 | semidirect |
| 9. C2×#100×C37 | C2 | semidirect |
| 13. #11924569 | C22 | semidirect |
| 15. #11924564 | C22 | semidirect |
| 22. C2×#10596940 | C22 | semidirect |
| 24. C2×#10596939 | C22 | semidirect |
| 25. #11924544 | C22 | semidirect |
| 30. #11924471 | C22 | semidirect |
| 31. #11924454 | C22 | semidirect |
| 32. #11924452 | C22 | semidirect |
| 36. #100×C37 | C22 | semidirect |
| 156. C2×#100 | D37 | semidirect |
| 157. C37 | #3068 | semidirect |
| 184. #100 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558333 | 2 |
| C2×#11924562 | 2 |
| #14558299 | 2 |
| #14557802 | 2 |
| #14557795 | 2 |
| #14557581 | 2 |
| #14557515 | 2 |
| C2×#100×C37 | 2 |
| #3068 | 37 |