Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
616 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 157 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. C22×#10596939 | C2 | semidirect |
| 2. C22×C8×D37 | C2 | semidirect |
| 3. C2×#11924511 | C2 | semidirect |
| 4. C2×#11924507 | C2 | semidirect |
| 5. #14557768 | C2 | direct (N × H) |
| 6. C2×#11924469 | C2 | semidirect |
| 7. C2×#11924458 | C2 | semidirect |
| 8. C2×#102×C37 | C2 | semidirect |
| 14. C2×#10596939 | C22 | semidirect |
| 17. C2×C8×D37 | C22 | semidirect |
| 19. #11924511 | C22 | semidirect |
| 21. #11924507 | C22 | semidirect |
| 25. #11924469 | C22 | semidirect |
| 26. #11924458 | C22 | semidirect |
| 30. #102×C37 | C22 | semidirect |
| 63. C2×#64436 | D4 | semidirect |
| 77. C22×D37 | D8 | semidirect |
| 101. #64436 | C2×D4 | semidirect |
| 117. C2×D37 | C2×D8 | semidirect |
| 126. C2×C37 | #466 | semidirect |
| 139. C2×#102 | D37 | semidirect |
| 140. C37 | C2×#466 | semidirect |
| 162. #102 | C2×D37 | semidirect |
| 259. C2 | #14557768 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10596939 | 2 |
| C22×C8×D37 | 2 |
| C2×#11924511 | 2 |
| C2×#11924507 | 2 |
| #14557768 | 2 |
| C2×#11924469 | 2 |
| C2×#11924458 | 2 |
| C2×#102×C37 | 2 |
| C2×#466 | 37 |