Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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 |
|---|---|---|
| 2. C22×#10596941 | C2 | semidirect |
| 3. C2×#11924543 | C2 | semidirect |
| 4. #14557798 | C2 | direct (N × H) |
| 5. C2×#11924471 | C2 | semidirect |
| 6. C2×#11924455 | C2 | semidirect |
| 7. C2×#11924452 | C2 | semidirect |
| 8. C2×#137×C37 | C2 | semidirect |
| 16. C2×#10596941 | C22 | semidirect |
| 19. #11924543 | C22 | semidirect |
| 25. #11924471 | C22 | semidirect |
| 26. #11924455 | C22 | semidirect |
| 27. #11924452 | C22 | semidirect |
| 31. #137×C37 | C22 | semidirect |
| 136. C2×C37 | #471 | semidirect |
| 139. C2×#137 | D37 | semidirect |
| 147. C37 | C2×#471 | semidirect |
| 152. #137 | C2×D37 | semidirect |
| 275. C2 | #14557798 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924561 | 2 |
| C22×#10596941 | 2 |
| C2×#11924543 | 2 |
| #14557798 | 2 |
| C2×#11924471 | 2 |
| C2×#11924455 | 2 |
| C2×#11924452 | 2 |
| C2×#137×C37 | 2 |
| C2×#471 | 37 |