Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
524 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 524 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. C22×#10596939 | C2 | semidirect |
| 2. C2×#11924543 | C2 | semidirect |
| 3. #14558097 | C2 | semidirect |
| 4. #14557784 | C2 | semidirect |
| 5. #14557767 | C2 | semidirect |
| 6. #14557569 | C2 | semidirect |
| 7. #14557538 | C2 | semidirect |
| 8. #14557537 | C2 | semidirect |
| 9. C37×#535 | C2 | semidirect |
| 16. C2×#10596934 | C22 | semidirect |
| 18. C22×#64436 | C22 | semidirect |
| 21. #11924510 | C22 | semidirect |
| 24. #11924469 | C22 | semidirect |
| 25. #11924467 | C22 | semidirect |
| 26. #11924457 | C22 | semidirect |
| 27. #11924456 | C22 | semidirect |
| 32. #121×C37 | C22 | semidirect |
| 67. C2×#64436 | D4 | semidirect |
| 129. #535 | D37 | semidirect |
| 135. C37 | #3058 | semidirect |
| 152. #121 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596939 | 2 |
| C2×#11924543 | 2 |
| #14558097 | 2 |
| #14557784 | 2 |
| #14557767 | 2 |
| #14557569 | 2 |
| #14557538 | 2 |
| #14557537 | 2 |
| C37×#535 | 2 |
| #3058 | 37 |