Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
596 conjugacy classes of subgroups; only the 135 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 135 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×D8×D43 | C2 | semidirect |
| 2. C2×M16×D43 | C2 | semidirect |
| 3. #121×D43 | C2 | semidirect |
| 4. #14583153 | C2 | semidirect |
| 5. #14583152 | C2 | semidirect |
| 6. #14583151 | C2 | semidirect |
| 7. #14583150 | C2 | semidirect |
| 8. #14583149 | C2 | semidirect |
| 9. #106×D43 | C2 | semidirect |
| 10. #102×D43 | C2 | semidirect |
| 11. C43×#469 | C2 | semidirect |
| 15. C2×D344 | C22 | semidirect |
| 16. C2×#10621882 | C22 | semidirect |
| 18. C2×#10621877 | C22 | semidirect |
| 19. C2×#10621872 | C22 | semidirect |
| 20. C2×#10621872 | C22 | semidirect |
| 24. #13063300 | C22 | semidirect |
| 25. #13063299 | C22 | semidirect |
| 28. #13063296 | C22 | semidirect |
| 31. #13063257 | C22 | semidirect |
| 32. #13063256 | C22 | semidirect |
| 33. #13063247 | C22 | semidirect |
| 34. #13063246 | C22 | semidirect |
| 35. #13063245 | C22 | semidirect |
| 36. C2×D8×C43 | C22 | semidirect |
| 37. C2×M16×C43 | C22 | semidirect |
| 38. #121×C43 | C22 | semidirect |
| 39. #106×C43 | C22 | semidirect |
| 40. #102×C43 | C22 | semidirect |
| 81. C8×D43 | D4 | semidirect |
| 118. C8×C43 | C2×D4 | semidirect |
| 120. C43⋊C8 | C2×D4 | semidirect |
| 150. D43 | #469 | direct (N × H) |
| 159. #469 | D43 | direct (N × H) |
| 162. C43 | C2×#469 | semidirect |
| 169. C2×D8 | C2×D43 | semidirect |
| 174. C2×M16 | C2×D43 | semidirect |
| 182. #121 | C2×D43 | semidirect |
| 187. #106 | C2×D43 | semidirect |
| 191. #102 | C2×D43 | semidirect |
| 271. C8 | D4×D43 | semidirect |