Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 133 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. #14558164 | C2 | semidirect |
| 3. #14557836 | C2 | semidirect |
| 4. #14557832 | C2 | semidirect |
| 5. #14557822 | C2 | semidirect |
| 6. #14557812 | C2 | semidirect |
| 7. #14557569 | C2 | semidirect |
| 8. #14557561 | C2 | semidirect |
| 11. C37×#428 | C2 | semidirect |
| 15. #11924535 | C22 | semidirect |
| 17. #11924527 | C22 | semidirect |
| 26. #11924469 | C22 | semidirect |
| 27. #11924469 | C22 | semidirect |
| 28. #11924467 | C22 | semidirect |
| 29. #11924467 | C22 | semidirect |
| 30. #11924465 | C22 | semidirect |
| 31. #11924465 | C22 | semidirect |
| 39. #107×C37 | C22 | semidirect |
| 40. #106×C37 | C22 | semidirect |
| 46. C2×D148 | Q8 | semidirect |
| 131. #428 | D37 | semidirect |
| 136. C37 | #3081 | semidirect |
| 156. #107 | C2×D37 | semidirect |
| 159. #106 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558164 | 2 |
| #14558007 | 2 |
| #14557836 | 2 |
| #14557832 | 2 |
| #14557822 | 2 |
| #14557812 | 2 |
| #14557569 | 2 |
| #14557561 | 2 |
| #14557539 | 2 |
| C2×#11924456 | 2 |
| C37×#428 | 2 |
| #3081 | 37 |