Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
468 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 468 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×#11924566 | C2 | semidirect |
| 3. C22×#10596930 | C2 | semidirect |
| 4. #14557796 | C2 | direct (N × H) |
| 5. C2×#11924472 | C2 | semidirect |
| 6. C2×#11924454 | C2 | semidirect |
| 7. C2×#11924452 | C2 | semidirect |
| 8. C2×#131×C37 | C2 | semidirect |
| 12. #11924566 | C22 | semidirect |
| 19. C2×#10596930 | C22 | semidirect |
| 25. #11924472 | C22 | semidirect |
| 26. #11924454 | C22 | semidirect |
| 27. #11924452 | C22 | semidirect |
| 30. #131×C37 | C22 | semidirect |
| 136. C2×C37 | #471 | semidirect |
| 142. C2×#131 | D37 | semidirect |
| 147. C37 | C2×#471 | semidirect |
| 164. #131 | C2×D37 | semidirect |
| 275. C2 | #14557796 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924566 | 2 |
| C2×#11924561 | 2 |
| C22×#10596930 | 2 |
| #14557796 | 2 |
| C2×#11924472 | 2 |
| C2×#11924454 | 2 |
| C2×#11924452 | 2 |
| C2×#131×C37 | 2 |
| C2×#471 | 37 |