Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
360 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 115 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×Q16×D37 | C2 | semidirect |
| 3. #14557976 | C2 | semidirect |
| 4. #14557975 | C2 | semidirect |
| 5. #14557974 | C2 | semidirect |
| 6. #14557973 | C2 | semidirect |
| 7. #14557972 | C2 | semidirect |
| 8. Q32×D37 | C2 | semidirect |
| 9. SD32×D37 | C2 | semidirect |
| 10. M32×D37 | C2 | semidirect |
| 11. C37×#510 | C2 | semidirect |
| 19. C2×Dic148 | C22 | semidirect |
| 25. Q16×D37 | C22 | semidirect |
| 29. Dic296 | C22 | semidirect |
| 30. #11924482 | C22 | semidirect |
| 31. #11924482 | C22 | semidirect |
| 32. #11924481 | C22 | semidirect |
| 33. #11924480 | C22 | semidirect |
| 34. #11924479 | C22 | semidirect |
| 35. #11924476 | C22 | semidirect |
| 36. #11924475 | C22 | semidirect |
| 39. C2×Q16×C37 | C22 | semidirect |
| 40. Q32×C37 | C22 | semidirect |
| 41. SD32×C37 | C22 | semidirect |
| 42. M32×C37 | C22 | semidirect |
| 144. D37 | #510 | direct (N × H) |
| 152. #510 | D37 | direct (N × H) |
| 156. C37 | C2×#510 | semidirect |
| 172. C2×Q16 | C2×D37 | semidirect |
| 179. Q32 | C2×D37 | semidirect |
| 183. SD32 | C2×D37 | semidirect |
| 186. M32 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #135×D37 | 2 |
| C2×Q16×D37 | 2 |
| #14557976 | 2 |
| #14557975 | 2 |
| #14557974 | 2 |
| #14557973 | 2 |
| #14557972 | 2 |
| Q32×D37 | 2 |
| SD32×D37 | 2 |
| M32×D37 | 2 |
| C37×#510 | 2 |
| C2×#510 | 37 |