Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063371 | C2 | semidirect |
| 2. C22×#10621882 | C2 | semidirect |
| 3. #14583466 | C2 | semidirect |
| 4. #14583043 | C2 | semidirect |
| 5. #14583031 | C2 | semidirect |
| 6. #14582905 | C2 | semidirect |
| 7. #14582895 | C2 | semidirect |
| 8. #14582867 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C43 | C2 | semidirect |
| 12. C2×#10621902 | C22 | semidirect |
| 18. C2×D4×D43 | C22 | semidirect |
| 20. C2×#10621882 | C22 | semidirect |
| 21. C22×C43⋊C8 | C22 | semidirect |
| 24. #13063296 | C22 | semidirect |
| 26. #13063284 | C22 | semidirect |
| 27. #13063249 | C22 | semidirect |
| 28. #13063247 | C22 | semidirect |
| 29. #13063246 | C22 | semidirect |
| 30. (C2×D43)⋊C8 | C22 | semidirect |
| 32. C22×D4×C43 | C22 | semidirect |
| 34. C2×SD16×C43 | C22 | semidirect |
| 35. C2×D8×C43 | C22 | semidirect |
| 36. C2×M16×C43 | C22 | semidirect |
| 41. #41×C43 | D4 | semidirect |
| 67. C2×D172 | D4 | semidirect |
| 153. C2×AGL(1,ℤ/8) | D43 | semidirect |
| 161. C43 | #3008 | semidirect |
| 172. C22×D4 | C2×D43 | semidirect |
| 174. C2×SD16 | C2×D43 | semidirect |
| 177. C2×D8 | C2×D43 | semidirect |
| 178. C2×M16 | C2×D43 | semidirect |
| 198. #41 | C22⋊D43 | semidirect |