Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
492 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #14557631 | C2 | semidirect |
| 4. C4×#10596941 | C2 | semidirect |
| 5. #14557569 | C2 | semidirect |
| 6. #14557542 | C2 | semidirect |
| 8. #14557489 | C2 | semidirect |
| 9. C37×#519 | C2 | semidirect |
| 11. C2×#10596941 | C4 | semidirect |
| 20. #11924469 | C22 | semidirect |
| 21. #11924467 | C22 | semidirect |
| 22. #11924460 | C22 | semidirect |
| 24. #11924447 | C22 | semidirect |
| 25. C4×#64436 | C22 | semidirect |
| 28. C4×Q8×C37 | C22 | semidirect |
| 35. C2×Q8×C37 | C2×C4 | semidirect |
| 53. #10596941 | C2×C4 | semidirect |
| 54. #10596941 | C2×C4 | semidirect |
| 59. C2×#64436 | C2×C4 | semidirect |
| 105. #519 | D37 | semidirect |
| 113. C37 | #2949 | semidirect |
| 122. C4×Q8 | C2×D37 | semidirect |
| 139. C2×Q8 | C4×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596941 | 2 |
| #14558007 | 2 |
| #14557631 | 2 |
| C4×#10596941 | 2 |
| #14557569 | 2 |
| #14557542 | 2 |
| #14557537 | 2 |
| #14557489 | 2 |
| C37×#519 | 2 |
| #2949 | 37 |