Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14583701 | C2 | semidirect |
| 2. #14583700 | C2 | semidirect |
| 3. #14583337 | C2 | semidirect |
| 4. #14583336 | C2 | semidirect |
| 5. #14583333 | C2 | semidirect |
| 6. #14583330 | C2 | semidirect |
| 7. #14583329 | C2 | semidirect |
| 8. C2×#13063266 | C2 | semidirect |
| 9. D16×D43 | C2 | semidirect |
| 10. #14583317 | C2 | semidirect |
| 11. C43×#509 | C2 | semidirect |
| 18. #13063348 | C22 | semidirect |
| 19. #13063347 | C22 | semidirect |
| 20. #13063344 | C22 | semidirect |
| 21. C2×D344 | C22 | semidirect |
| 22. D8×D43 | C22 | semidirect |
| 23. D8×D43 | C22 | semidirect |
| 25. #13063271 | C22 | semidirect |
| 26. #13063270 | C22 | semidirect |
| 27. #13063269 | C22 | semidirect |
| 28. #13063268 | C22 | semidirect |
| 29. D688 | C22 | semidirect |
| 30. #13063266 | C22 | semidirect |
| 31. #13063266 | C22 | semidirect |
| 32. #13063266 | C22 | semidirect |
| 33. #13063264 | C22 | semidirect |
| 34. C2×C43⋊C16 | C22 | semidirect |
| 35. C16×D43 | C22 | semidirect |
| 36. #135×C43 | C22 | semidirect |
| 37. C2×D8×C43 | C22 | semidirect |
| 38. SD32×C43 | C22 | semidirect |
| 39. D16×C43 | C22 | semidirect |
| 40. M32×C43 | C22 | semidirect |
| 135. #509 | D43 | semidirect |
| 141. C43 | #3415 | semidirect |
| 151. #135 | C2×D43 | semidirect |
| 155. C2×D8 | C2×D43 | semidirect |
| 161. SD32 | C2×D43 | semidirect |
| 166. D16 | C2×D43 | semidirect |
| 168. M32 | C2×D43 | semidirect |