Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
368 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 368 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 |
|---|---|---|
| 1. #135×D43 | C2 | semidirect |
| 2. #14583332 | C2 | semidirect |
| 3. #14583331 | C2 | semidirect |
| 4. #14583330 | C2 | semidirect |
| 5. #14583329 | C2 | semidirect |
| 6. #14583328 | C2 | semidirect |
| 7. Q32×D43 | C2 | semidirect |
| 8. SD32×D43 | C2 | semidirect |
| 9. D16×D43 | C2 | semidirect |
| 10. C2×C16×D43 | C2 | semidirect |
| 11. C43×#508 | C2 | semidirect |
| 13. #13063348 | C22 | semidirect |
| 14. #13063347 | C22 | semidirect |
| 17. #13063344 | C22 | semidirect |
| 22. Dic344 | C22 | semidirect |
| 23. #13063271 | C22 | semidirect |
| 24. #13063270 | C22 | semidirect |
| 25. #13063269 | C22 | semidirect |
| 26. #13063268 | C22 | semidirect |
| 27. D688 | C22 | semidirect |
| 28. #13063266 | C22 | semidirect |
| 29. C2×C43⋊C16 | C22 | semidirect |
| 32. C16×D43 | C22 | semidirect |
| 33. C16×D43 | C22 | semidirect |
| 34. #135×C43 | C22 | semidirect |
| 35. Q32×C43 | C22 | semidirect |
| 36. SD32×C43 | C22 | semidirect |
| 37. D16×C43 | C22 | semidirect |
| 38. C2×C16×C43 | C22 | semidirect |
| 116. D43 | #508 | direct (N × H) |
| 123. #508 | D43 | direct (N × H) |
| 128. C43 | C2×#508 | semidirect |
| 135. #135 | C2×D43 | semidirect |
| 142. Q32 | C2×D43 | semidirect |
| 146. SD32 | C2×D43 | semidirect |
| 149. D16 | C2×D43 | semidirect |
| 155. C2×C16 | C2×D43 | semidirect |