Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#11924543 | C2 | semidirect |
| 3. #14558097 | C2 | semidirect |
| 4. #14557784 | C2 | semidirect |
| 5. #14557781 | C2 | semidirect |
| 6. #14557767 | C2 | semidirect |
| 7. #14557764 | C2 | semidirect |
| 8. #14557573 | C2 | semidirect |
| 9. #14557529 | C2 | semidirect |
| 10. C2×#11924456 | C2 | semidirect |
| 11. C37×#537 | C2 | semidirect |
| 18. C2×#10596934 | C22 | semidirect |
| 20. C22×#64436 | C22 | semidirect |
| 27. #11924469 | C22 | semidirect |
| 28. #11924467 | C22 | semidirect |
| 29. #11924460 | C22 | semidirect |
| 30. #11924460 | C22 | semidirect |
| 31. #11924457 | C22 | semidirect |
| 32. #11924457 | C22 | semidirect |
| 38. C22⋊Q8×C37 | C22 | semidirect |
| 41. #121×C37 | C22 | semidirect |
| 79. #10596934 | D4 | semidirect |
| 154. #537 | D37 | semidirect |
| 163. C37 | #3062 | semidirect |
| 178. C22⋊Q8 | C2×D37 | semidirect |
| 183. #121 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924561 | 2 |
| C2×#11924543 | 2 |
| #14558097 | 2 |
| #14557784 | 2 |
| #14557781 | 2 |
| #14557767 | 2 |
| #14557764 | 2 |
| #14557573 | 2 |
| #14557529 | 2 |
| C2×#11924456 | 2 |
| C37×#537 | 2 |
| #3062 | 37 |