Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
524 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 524 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. C22×#10596939 | C2 | semidirect |
| 2. C2×#11924544 | C2 | semidirect |
| 3. #14558102 | C2 | semidirect |
| 4. #14558100 | C2 | semidirect |
| 5. #14557785 | C2 | semidirect |
| 6. #14557768 | C2 | semidirect |
| 7. #14557569 | C2 | semidirect |
| 8. #14557539 | C2 | semidirect |
| 9. C37×#418 | C2 | semidirect |
| 16. C2×#10596929 | C22 | semidirect |
| 18. C2×C8×D37 | C22 | semidirect |
| 23. #11924511 | C22 | semidirect |
| 24. #11924507 | C22 | semidirect |
| 28. #11924469 | C22 | semidirect |
| 29. #11924467 | C22 | semidirect |
| 30. #11924458 | C22 | semidirect |
| 34. #102×C37 | C22 | semidirect |
| 66. C2×#64436 | D4 | semidirect |
| 134. #418 | D37 | semidirect |
| 135. C37 | #3058 | semidirect |
| 160. #102 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596939 | 2 |
| C2×#11924544 | 2 |
| #14558102 | 2 |
| #14558100 | 2 |
| #14557785 | 2 |
| #14557768 | 2 |
| #14557569 | 2 |
| #14557539 | 2 |
| C37×#418 | 2 |
| #3058 | 37 |