Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 149 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. C22×#10596930 | C2 | semidirect |
| 2. #14558104 | C2 | semidirect |
| 4. #14557779 | C2 | semidirect |
| 5. #14557762 | C2 | semidirect |
| 6. #14557571 | C2 | semidirect |
| 7. #14557543 | C2 | semidirect |
| 8. #14557539 | C2 | semidirect |
| 9. C2×#131×C37 | C2 | semidirect |
| 20. #11924515 | C22 | semidirect |
| 25. #11924470 | C22 | semidirect |
| 26. #11924468 | C22 | semidirect |
| 27. #11924461 | C22 | semidirect |
| 32. C2×M16×C37 | C22 | semidirect |
| 34. C22×C8×C37 | C22 | semidirect |
| 56. C2×C8×C37 | D4 | semidirect |
| 122. C2×#131 | D37 | semidirect |
| 130. C37 | #3057 | semidirect |
| 139. C2×M16 | C2×D37 | semidirect |
| 141. C22×C8 | C2×D37 | semidirect |
| 179. C2×C8 | C22⋊D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596930 | 2 |
| #14558104 | 2 |
| #14558097 | 2 |
| #14557779 | 2 |
| #14557762 | 2 |
| #14557571 | 2 |
| #14557543 | 2 |
| #14557539 | 2 |
| C2×#131×C37 | 2 |
| #3057 | 37 |