Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
548 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 143 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×M16×D43 | C2 | semidirect |
| 2. #14583406 | C2 | semidirect |
| 3. C2×#13063296 | C2 | semidirect |
| 4. #14583149 | C2 | semidirect |
| 5. #14583142 | C2 | semidirect |
| 6. #14583132 | C2 | semidirect |
| 7. #14583125 | C2 | semidirect |
| 8. #14582941 | C2 | semidirect |
| 9. #14582904 | C2 | semidirect |
| 10. #14582900 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C43 | C2 | semidirect |
| 15. C2×#10621872 | C22 | semidirect |
| 17. C2×C8×D43 | C22 | semidirect |
| 19. #13063301 | C22 | semidirect |
| 20. #13063301 | C22 | semidirect |
| 25. #13063296 | C22 | semidirect |
| 26. #13063296 | C22 | semidirect |
| 33. #13063259 | C22 | semidirect |
| 34. #13063257 | C22 | semidirect |
| 35. #13063249 | C22 | semidirect |
| 36. #13063246 | C22 | semidirect |
| 37. #13063246 | C22 | semidirect |
| 38. #13063246 | C22 | semidirect |
| 42. C2×SD16×C43 | C22 | semidirect |
| 43. C2×D8×C43 | C22 | semidirect |
| 73. M16×C43 | D4 | semidirect |
| 135. C8×C43 | C2×D4 | semidirect |
| 154. C2×D43 | AGL(1,ℤ/8) | semidirect |
| 173. C2×AGL(1,ℤ/8) | D43 | semidirect |
| 184. C43 | #3055 | semidirect |
| 190. C2×SD16 | C2×D43 | semidirect |
| 191. C2×D8 | C2×D43 | semidirect |
| 248. M16 | C22⋊D43 | semidirect |
| 309. C8 | C2×C22⋊D43 | semidirect |