Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
468 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 468 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×#11924567 | C2 | semidirect |
| 3. C22×#10596941 | C2 | semidirect |
| 4. C2×#11924544 | C2 | semidirect |
| 5. #14557799 | C2 | direct (N × H) |
| 6. C2×#11924471 | C2 | semidirect |
| 7. C2×#11924452 | C2 | semidirect |
| 8. C2×#101×C37 | C2 | semidirect |
| 12. #11924567 | C22 | semidirect |
| 21. C2×#10596941 | C22 | semidirect |
| 24. #11924544 | C22 | semidirect |
| 29. #11924471 | C22 | semidirect |
| 30. #11924452 | C22 | semidirect |
| 34. #101×C37 | C22 | semidirect |
| 135. C2×C37 | #471 | semidirect |
| 145. C2×#101 | D37 | semidirect |
| 147. C37 | C2×#471 | semidirect |
| 172. #101 | C2×D37 | semidirect |
| 275. C2 | #14557799 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924567 | 2 |
| C2×#11924564 | 2 |
| C22×#10596941 | 2 |
| C2×#11924544 | 2 |
| #14557799 | 2 |
| C2×#11924471 | 2 |
| C2×#11924452 | 2 |
| C2×#101×C37 | 2 |
| C2×#471 | 37 |