Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 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. C2×#13063344 | C2 | semidirect |
| 2. #135×D43 | C2 | semidirect |
| 3. #14583342 | C2 | semidirect |
| 4. #14583339 | C2 | semidirect |
| 5. #14583338 | C2 | semidirect |
| 6. #14583335 | C2 | semidirect |
| 7. #14583333 | C2 | semidirect |
| 8. #14583330 | C2 | semidirect |
| 9. #14583328 | C2 | semidirect |
| 10. M32×D43 | C2 | semidirect |
| 11. C43×#509 | C2 | semidirect |
| 14. #13063348 | C22 | semidirect |
| 21. #13063344 | C22 | semidirect |
| 22. #13063344 | C22 | semidirect |
| 23. C2×Dic172 | C22 | semidirect |
| 24. Q16×D43 | C22 | semidirect |
| 27. D8×D43 | C22 | semidirect |
| 29. Dic344 | C22 | semidirect |
| 30. #13063271 | C22 | semidirect |
| 31. #13063270 | C22 | semidirect |
| 32. #13063269 | C22 | semidirect |
| 33. #13063269 | C22 | semidirect |
| 34. #13063266 | C22 | semidirect |
| 35. #13063265 | C22 | semidirect |
| 36. #13063264 | C22 | semidirect |
| 37. C16×D43 | C22 | semidirect |
| 39. C2×D8×C43 | C22 | semidirect |
| 40. SD32×C43 | C22 | semidirect |
| 41. D16×C43 | C22 | semidirect |
| 42. M32×C43 | C22 | semidirect |
| 154. #509 | D43 | semidirect |
| 158. C43 | #3414 | semidirect |
| 176. C2×D8 | C2×D43 | semidirect |
| 183. SD32 | C2×D43 | semidirect |
| 185. D16 | C2×D43 | semidirect |
| 188. M32 | C2×D43 | semidirect |