Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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×#10596929 | C2 | semidirect |
| 3. C2×#11924494 | C2 | semidirect |
| 4. #14557536 | C2 | direct (N × H) |
| 5. C2×#11924458 | C2 | semidirect |
| 6. C2×#11924457 | C2 | semidirect |
| 7. C2×#11924456 | C2 | semidirect |
| 8. C2×#102×C37 | C2 | semidirect |
| 14. C2×D4×D37 | C4 | semidirect |
| 18. C2×#10596929 | C22 | semidirect |
| 19. C22×#64436 | C22 | semidirect |
| 21. #11924494 | C22 | semidirect |
| 22. C2×C4⋊Dic37 | C22 | semidirect |
| 25. #11924458 | C22 | semidirect |
| 26. #11924457 | C22 | semidirect |
| 27. #11924456 | C22 | semidirect |
| 29. C22×C8×C37 | C22 | semidirect |
| 30. C2×C4⋊C4×C37 | C22 | semidirect |
| 31. #102×C37 | C22 | semidirect |
| 51. D4×D37 | C2×C4 | semidirect |
| 61. C2×C8×C37 | C23 | semidirect |
| 63. C4⋊C4×C37 | C23 | semidirect |
| 66. C4⋊Dic37 | C23 | semidirect |
| 69. C2×#64436 | C23 | semidirect |
| 135. C2×C37 | #418 | semidirect |
| 148. C2×#102 | D37 | semidirect |
| 149. C37 | C2×#418 | semidirect |
| 162. C22×C8 | C2×D37 | semidirect |
| 166. C2×C4⋊C4 | C2×D37 | semidirect |
| 172. #102 | C2×D37 | semidirect |
| 205. C2×C8 | C22×D37 | semidirect |
| 209. C4⋊C4 | C22×D37 | semidirect |
| 277. C2 | #14557536 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D4×D37 | 2 |
| C22×#10596929 | 2 |
| C2×#11924494 | 2 |
| #14557536 | 2 |
| C2×#11924458 | 2 |
| C2×#11924457 | 2 |
| C2×#11924456 | 2 |
| C2×#102×C37 | 2 |
| C2×#418 | 37 |