Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
616 conjugacy classes of subgroups; only the 221 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 221 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 |
|---|---|---|
| 2. C2×C4×D172 | C2 | semidirect |
| 3. C4×#10621882 | C2 | direct (N × H) |
| 4. C2×#13063258 | C2 | semidirect |
| 5. C2×#13063246 | C2 | semidirect |
| 6. C2×#13063245 | C2 | semidirect |
| 7. C2×C4×C43⋊C8 | C2 | semidirect |
| 8. C2×C4×D4×C43 | C2 | semidirect |
| 11. C2×#10621882 | C4 | direct (N × H) |
| 16. C4×D172 | C22 | semidirect |
| 19. #13063258 | C22 | semidirect |
| 20. #13063246 | C22 | semidirect |
| 21. #13063245 | C22 | semidirect |
| 22. C4×C43⋊C8 | C22 | semidirect |
| 26. C4×D4×C43 | C22 | semidirect |
| 34. C2×D4×C43 | C2×C4 | semidirect |
| 45. C2×D172 | C2×C4 | semidirect |
| 54. #10621882 | C2×C4 | direct (N × H) |
| 59. C2×C43⋊C8 | C2×C4 | semidirect |
| 73. D4×C43 | C22×C4 | semidirect |
| 78. C2×C4×C43 | D8 | semidirect |
| 89. D172 | C22×C4 | semidirect |
| 92. C43⋊C8 | C22×C4 | semidirect |
| 108. C4×C43 | C2×D8 | semidirect |
| 114. C2×C43 | C4×D8 | semidirect |
| 121. C2×C4×D4 | D43 | semidirect |
| 127. C43 | C2×C4×D8 | semidirect |
| 139. C4×D4 | C2×D43 | semidirect |
| 157. C2×D4 | C4×D43 | semidirect |
| 195. D4 | C2×C4×D43 | semidirect |
| 203. C2×C4 | #10621882 | direct (N × H) |
| 228. C4 | C2×#10621882 | direct (N × H) |
| 233. C2 | C4×#10621882 | direct (N × H) |