Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
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×D43 | C2 | semidirect |
| 3. #14583342 | C2 | semidirect |
| 4. #14583341 | C2 | semidirect |
| 5. #14583340 | C2 | semidirect |
| 6. #14583339 | C2 | semidirect |
| 7. #14583338 | C2 | semidirect |
| 8. Q32×D43 | C2 | semidirect |
| 9. SD32×D43 | C2 | semidirect |
| 10. M32×D43 | C2 | semidirect |
| 11. C43×#510 | C2 | semidirect |
| 19. C2×Dic172 | C22 | semidirect |
| 25. Q16×D43 | C22 | semidirect |
| 29. Dic344 | C22 | semidirect |
| 30. #13063271 | C22 | semidirect |
| 31. #13063271 | C22 | semidirect |
| 32. #13063270 | C22 | semidirect |
| 33. #13063269 | C22 | semidirect |
| 34. #13063268 | C22 | semidirect |
| 35. #13063265 | C22 | semidirect |
| 36. #13063264 | C22 | semidirect |
| 39. C2×Q16×C43 | C22 | semidirect |
| 40. Q32×C43 | C22 | semidirect |
| 41. SD32×C43 | C22 | semidirect |
| 42. M32×C43 | C22 | semidirect |
| 144. D43 | #510 | direct (N × H) |
| 152. #510 | D43 | direct (N × H) |
| 156. C43 | C2×#510 | semidirect |
| 172. C2×Q16 | C2×D43 | semidirect |
| 179. Q32 | C2×D43 | semidirect |
| 183. SD32 | C2×D43 | semidirect |
| 186. M32 | C2×D43 | semidirect |