Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
994 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 994 conjugacy classes of subgroups — too many to draw. Only its 157 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. C23×D172 | C2 | semidirect |
| 2. C2×#13063350 | C2 | semidirect |
| 3. #14583049 | C2 | semidirect |
| 4. #14583032 | C2 | semidirect |
| 5. #14582903 | C2 | semidirect |
| 6. #14582863 | C2 | semidirect |
| 7. C43×#525 | C2 | semidirect |
| 15. C2×#10621884 | C22 | semidirect |
| 16. C2×#10621882 | C22 | semidirect |
| 17. C2×#10621877 | C22 | semidirect |
| 18. #13063245 | C22 | semidirect |
| 19. C22⋊(C43⋊C8) | C22 | semidirect |
| 20. C2×#41×C43 | C22 | semidirect |
| 23. C22⋊Q8×C43 | C22 | semidirect |
| 24. #121×C43 | C22 | semidirect |
| 27. #117×C43 | C22 | semidirect |
| 34. C2×Q8×C43 | C23 | semidirect |
| 37. C2×D4×C43 | C23 | semidirect |
| 50. C2×D172 | D4 | semidirect |
| 53. C4⋊C4×C43 | C23 | semidirect |
| 61. C2×C43⋊C8 | C23 | semidirect |
| 100. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 120. #525 | D43 | semidirect |
| 125. C43 | #3003 | semidirect |
| 127. C2×#41 | C2×D43 | semidirect |
| 139. C22⋊Q8 | C2×D43 | semidirect |
| 140. #121 | C2×D43 | semidirect |
| 143. #117 | C2×D43 | semidirect |
| 152. C2×Q8 | C22×D43 | semidirect |
| 163. C2×D4 | C22×D43 | semidirect |
| 175. C4⋊C4 | C22×D43 | semidirect |
| 222. C22 | #13063350 | semidirect |