Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
350 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 350 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14558347 | C2 | semidirect |
| 2. #14558346 | C2 | semidirect |
| 3. #14557976 | C2 | semidirect |
| 4. #14557975 | C2 | semidirect |
| 5. #14557972 | C2 | semidirect |
| 6. #14557964 | C2 | semidirect |
| 7. #14557963 | C2 | semidirect |
| 8. C2×#11924482 | C2 | semidirect |
| 9. Q32×D37 | C2 | semidirect |
| 10. #14557951 | C2 | semidirect |
| 11. C37×#510 | C2 | semidirect |
| 129. #510 | D37 | semidirect |
| 135. C37 | #3417 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558347 | 2 |
| #14558346 | 2 |
| #14557976 | 2 |
| #14557975 | 2 |
| #14557972 | 2 |
| #14557964 | 2 |
| #14557963 | 2 |
| C2×#11924482 | 2 |
| Q32×D37 | 2 |
| #14557951 | 2 |
| C37×#510 | 2 |
| #3417 | 37 |