Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
488 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 488 conjugacy classes of subgroups — too many to draw. Only its 141 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×#11924561 | C2 | semidirect |
| 2. C22×#10596939 | C2 | semidirect |
| 3. C2×#11924543 | C2 | semidirect |
| 4. #14557801 | C2 | direct (N × H) |
| 5. C2×#11924471 | C2 | semidirect |
| 6. C2×#11924453 | C2 | semidirect |
| 7. C2×#11924452 | C2 | semidirect |
| 8. C2×AGL(1,ℤ/8)×C37 | C2 | semidirect |
| 11. #11924561 | C22 | semidirect |
| 17. C2×#10596939 | C22 | semidirect |
| 19. #11924543 | C22 | semidirect |
| 25. #11924471 | C22 | semidirect |
| 26. #11924453 | C22 | semidirect |
| 27. #11924452 | C22 | semidirect |
| 31. AGL(1,ℤ/8)×C37 | C22 | semidirect |
| 141. C2×C37 | #472 | semidirect |
| 145. C2×AGL(1,ℤ/8) | D37 | semidirect |
| 152. C37 | C2×#472 | semidirect |
| 159. AGL(1,ℤ/8) | C2×D37 | semidirect |
| 285. C2 | #14557801 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924561 | 2 |
| C22×#10596939 | 2 |
| C2×#11924543 | 2 |
| #14557801 | 2 |
| C2×#11924471 | 2 |
| C2×#11924453 | 2 |
| C2×#11924452 | 2 |
| C2×AGL(1,ℤ/8)×C37 | 2 |
| C2×#472 | 37 |