Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
732 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 732 conjugacy classes of subgroups — too many to draw. Only its 149 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×#11924583 | C2 | semidirect |
| 2. C2×#11924561 | C2 | semidirect |
| 3. C22×#10596930 | C2 | semidirect |
| 4. #14558102 | C2 | semidirect |
| 5. #14557679 | C2 | semidirect |
| 6. #14557673 | C2 | semidirect |
| 7. #14557541 | C2 | semidirect |
| 8. #14557499 | C2 | semidirect |
| 9. C37×#416 | C2 | semidirect |
| 15. C2×#10596964 | C22 | semidirect |
| 18. C2×Q8×D37 | C22 | semidirect |
| 30. #11924459 | C22 | semidirect |
| 31. #11924448 | C22 | semidirect |
| 35. #103×C37 | C22 | semidirect |
| 36. #102×C37 | C22 | semidirect |
| 39. #41×C37 | D4 | semidirect |
| 70. C2×Dic74 | D4 | semidirect |
| 153. #416 | D37 | semidirect |
| 155. C37 | #3010 | semidirect |
| 180. #103 | C2×D37 | semidirect |
| 181. #102 | C2×D37 | semidirect |
| 191. #41 | D148 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924583 | 2 |
| C2×#11924561 | 2 |
| C22×#10596930 | 2 |
| #14558102 | 2 |
| #14557679 | 2 |
| #14557673 | 2 |
| #14557541 | 2 |
| #14557499 | 2 |
| C37×#416 | 2 |
| #3010 | 37 |