Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #14558331 | C2 | semidirect |
| 2. C2×#11924562 | C2 | semidirect |
| 3. #14558300 | C2 | semidirect |
| 4. #14557801 | C2 | semidirect |
| 5. #14557794 | C2 | semidirect |
| 6. #14557581 | C2 | semidirect |
| 7. #14557515 | C2 | semidirect |
| 8. C2×#11924453 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C37 | C2 | semidirect |
| 12. #11924566 | C22 | semidirect |
| 16. #11924561 | C22 | semidirect |
| 18. C2×#10596940 | C22 | semidirect |
| 19. C2×#10596939 | C22 | semidirect |
| 21. #11924543 | C22 | semidirect |
| 26. #11924471 | C22 | semidirect |
| 27. #11924454 | C22 | semidirect |
| 28. #11924453 | C22 | semidirect |
| 29. #11924452 | C22 | semidirect |
| 150. C2×AGL(1,ℤ/8) | D37 | semidirect |
| 157. C37 | #3068 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558331 | 2 |
| C2×#11924562 | 2 |
| #14558300 | 2 |
| #14557801 | 2 |
| #14557794 | 2 |
| #14557581 | 2 |
| #14557515 | 2 |
| C2×#11924453 | 2 |
| C2×AGL(1,ℤ/8)×C37 | 2 |
| #3068 | 37 |