Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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. D4×D172 | C2 | semidirect |
| 3. #14583273 | C2 | semidirect |
| 4. #14583147 | C2 | semidirect |
| 5. #14583101 | C2 | semidirect |
| 6. #14583094 | C2 | semidirect |
| 7. #14583049 | C2 | semidirect |
| 8. #14583044 | C2 | semidirect |
| 9. C4×#10621882 | C2 | semidirect |
| 10. #14582977 | C2 | semidirect |
| 11. C43×#547 | C2 | semidirect |
| 16. C2×#10621884 | C22 | semidirect |
| 17. C2×#10621884 | C22 | semidirect |
| 19. C2×#10621882 | C22 | semidirect |
| 20. C2×#10621877 | C22 | semidirect |
| 26. #13063258 | C22 | semidirect |
| 27. C4⋊(C43⋊C8) | C22 | semidirect |
| 28. #13063249 | C22 | semidirect |
| 29. #13063246 | C22 | semidirect |
| 31. #13063245 | C22 | semidirect |
| 32. C22⋊(C43⋊C8) | C22 | semidirect |
| 33. C4×C43⋊C8 | C22 | semidirect |
| 34. C2×#41×C43 | C22 | semidirect |
| 35. C4⋊Q8×C43 | C22 | semidirect |
| 37. C22⋊Q8×C43 | C22 | semidirect |
| 40. C4×D4×C43 | C22 | semidirect |
| 75. #10621882 | D4 | semidirect |
| 95. D4×C43 | C2×D4 | semidirect |
| 118. C43⋊C8 | C2×D4 | semidirect |
| 137. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 150. #547 | D43 | semidirect |
| 160. C43 | #3272 | semidirect |
| 161. C2×#41 | C2×D43 | semidirect |
| 171. C4⋊Q8 | C2×D43 | semidirect |
| 174. C22⋊Q8 | C2×D43 | semidirect |
| 181. C4×D4 | C2×D43 | semidirect |
| 252. D4 | D4×D43 | semidirect |
| 287. C4 | #13063350 | semidirect |