Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
488 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 488 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. C2×#11924564 | C2 | semidirect |
| 2. C2×#11924562 | C2 | semidirect |
| 3. C22×#10596939 | C2 | semidirect |
| 4. C2×#11924544 | C2 | semidirect |
| 5. #14557802 | C2 | direct (N × H) |
| 6. C2×#11924471 | C2 | semidirect |
| 7. C2×#11924452 | C2 | semidirect |
| 8. C2×#100×C37 | C2 | semidirect |
| 12. #11924564 | C22 | semidirect |
| 14. #11924562 | C22 | semidirect |
| 22. C2×#10596939 | C22 | semidirect |
| 24. #11924544 | C22 | semidirect |
| 29. #11924471 | C22 | semidirect |
| 30. #11924452 | C22 | semidirect |
| 34. #100×C37 | C22 | semidirect |
| 140. C2×C37 | #472 | semidirect |
| 151. C2×#100 | D37 | semidirect |
| 152. C37 | C2×#472 | semidirect |
| 178. #100 | C2×D37 | semidirect |
| 285. C2 | #14557802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924564 | 2 |
| C2×#11924562 | 2 |
| C22×#10596939 | 2 |
| C2×#11924544 | 2 |
| #14557802 | 2 |
| C2×#11924471 | 2 |
| C2×#11924452 | 2 |
| C2×#100×C37 | 2 |
| C2×#472 | 37 |