Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
726 conjugacy classes of subgroups; only the 200 normal subgroups are shown.
This group has 726 conjugacy classes of subgroups — too many to draw. Only its 200 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. D37⋊#131 | C2 | semidirect |
| 2. #14558602 | C2 | semidirect |
| 3. #14558526 | C2 | semidirect |
| 4. #14558524 | C2 | semidirect |
| 5. #14558523 | C2 | semidirect |
| 6. C2×#11924599 | C2 | semidirect |
| 22. #11924584 | C4 | semidirect |
| 24. #11924583 | C4 | semidirect |
| 25. #11924583 | C4 | semidirect |
| 31. 2−1+4×C37 | C4 | semidirect |
| 35. #41×C37 | C2×C4 | semidirect |
| 37. C2×Q8×C37 | C2×C4 | semidirect |
| 39. #10596966 | C2×C4 | semidirect |
| 45. Q8×D37 | C2×C4 | semidirect |
| 51. #10596964 | C2×C4 | semidirect |
| 60. #10596962 | C2×C4 | semidirect |
| 66. C2×Dic74 | C2×C4 | semidirect |
| 149. C37 | #2898 | semidirect |
| 155. 2−1+4 | #3866 | semidirect |
| 189. #41 | C2×#3866 | semidirect |
| 201. C2×Q8 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D37⋊#131 | 2 |
| #14558602 | 2 |
| #14558526 | 2 |
| #14558524 | 2 |
| #14558523 | 2 |
| C2×#11924599 | 2 |
| 2−1+4×D37 | 2 |
| #2898 | 37 |