Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
784 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063350 | C2 | semidirect |
| 2. C22×#10621882 | C2 | semidirect |
| 3. #14583463 | C2 | semidirect |
| 4. #14583044 | C2 | semidirect |
| 5. #14583033 | C2 | semidirect |
| 6. #14582904 | C2 | semidirect |
| 7. #14582895 | C2 | semidirect |
| 8. #14582866 | C2 | semidirect |
| 9. C2×H(5,𝔽2)×C43 | C2 | semidirect |
| 10. C22×D172 | C22 | semidirect |
| 12. C2×#10621884 | C22 | semidirect |
| 14. C2×#10621882 | C22 | semidirect |
| 15. C2×#10621882 | C22 | semidirect |
| 16. C2×#10621877 | C22 | semidirect |
| 17. C22×C43⋊C8 | C22 | semidirect |
| 20. #13063299 | C22 | semidirect |
| 22. #13063284 | C22 | semidirect |
| 23. #13063249 | C22 | semidirect |
| 24. #13063246 | C22 | semidirect |
| 25. #13063246 | C22 | semidirect |
| 26. C22⋊(C43⋊C8) | C22 | semidirect |
| 32. C2×#41×C43 | C22 | semidirect |
| 36. C22×D4×C43 | C22 | semidirect |
| 46. #41×C43 | D4 | semidirect |
| 60. C2×D4×C43 | D4 | semidirect |
| 152. C2×H(5,𝔽2) | D43 | semidirect |
| 161. C43 | #3008 | semidirect |
| 167. C2×#41 | C2×D43 | semidirect |
| 172. C22×D4 | C2×D43 | semidirect |
| 198. #41 | C22⋊D43 | semidirect |
| 217. C2×D4 | C22⋊D43 | semidirect |