Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
546 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 546 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. C22×#10621883 | C2 | semidirect |
| 2. D4×Dic86 | C2 | semidirect |
| 3. #14583271 | C2 | semidirect |
| 4. #14583126 | C2 | semidirect |
| 5. #14583104 | C2 | semidirect |
| 6. #14583096 | C2 | semidirect |
| 7. #14583050 | C2 | semidirect |
| 8. #14583037 | C2 | semidirect |
| 9. C4×#10621883 | C2 | semidirect |
| 10. D4×C43⋊C8 | C2 | semidirect |
| 12. C22×Dic86 | C22 | semidirect |
| 16. C2×#10621883 | C22 | semidirect |
| 17. C2×#10621883 | C22 | semidirect |
| 18. C2×#10621883 | C22 | semidirect |
| 19. C22×C43⋊C8 | C22 | semidirect |
| 20. #13063325 | C22 | semidirect |
| 22. #13063304 | C22 | semidirect |
| 24. C4×Dic86 | C22 | semidirect |
| 26. #13063256 | C22 | semidirect |
| 27. C4⋊(C43⋊C8) | C22 | semidirect |
| 28. #13063248 | C22 | semidirect |
| 29. #13063248 | C22 | semidirect |
| 31. #13063246 | C22 | semidirect |
| 32. C22⋊(C43⋊C8) | C22 | semidirect |
| 33. C4×C43⋊C8 | C22 | semidirect |
| 72. #10621883 | D4 | direct (N × H) |
| 96. D4×C43 | SD16 | semidirect |
| 114. Dic86 | C2×D4 | semidirect |
| 117. C43⋊C8 | C2×D4 | semidirect |
| 127. C22×C43 | C2×SD16 | semidirect |
| 132. C4×C43 | C2×SD16 | semidirect |
| 156. C43 | D4×SD16 | semidirect |
| 246. D4 | #10621883 | direct (N × H) |
| 272. C22 | C2×#10621883 | semidirect |
| 280. C4 | C2×#10621883 | semidirect |