Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
708 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 708 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 |
|---|---|---|
| 2. C2×#11924567 | C2 | semidirect |
| 3. C2×#11924534 | C2 | semidirect |
| 4. #14557714 | C2 | direct (N × H) |
| 5. C2×#11924463 | C2 | semidirect |
| 6. C2×#11924462 | C2 | semidirect |
| 7. C2×#11924454 | C2 | semidirect |
| 8. C2×#137×C37 | C2 | semidirect |
| 21. #11924567 | C22 | semidirect |
| 26. #11924534 | C22 | semidirect |
| 29. #11924463 | C22 | semidirect |
| 30. #11924462 | C22 | semidirect |
| 31. #11924454 | C22 | semidirect |
| 35. #137×C37 | C22 | semidirect |
| 168. C2×C37 | #456 | semidirect |
| 173. C2×#137 | D37 | semidirect |
| 179. C37 | C2×#456 | semidirect |
| 196. #137 | C2×D37 | semidirect |
| 339. C2 | #14557714 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924583 | 2 |
| C2×#11924567 | 2 |
| C2×#11924534 | 2 |
| #14557714 | 2 |
| C2×#11924463 | 2 |
| C2×#11924462 | 2 |
| C2×#11924454 | 2 |
| C2×#137×C37 | 2 |
| C2×#456 | 37 |