Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 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. C2×#13063350 | C2 | semidirect |
| 2. C2×#13063322 | C2 | semidirect |
| 3. #14583289 | C2 | semidirect |
| 4. #14583275 | C2 | semidirect |
| 5. #14583273 | C2 | semidirect |
| 6. C4×#10621877 | C2 | semidirect |
| 7. C43×#532 | C2 | semidirect |
| 11. C2×#10621884 | C22 | semidirect |
| 12. C2×#10621882 | C22 | semidirect |
| 17. #13063236 | C22 | semidirect |
| 18. C4×C43⋊C8 | C22 | semidirect |
| 20. C4⋊Q8×C43 | C22 | semidirect |
| 21. #127×C43 | C22 | semidirect |
| 22. #124×C43 | C22 | semidirect |
| 48. #10621877 | D4 | semidirect |
| 71. C43⋊C8 | C2×D4 | semidirect |
| 83. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 92. #532 | D43 | semidirect |
| 98. C43 | #3151 | semidirect |
| 106. C4⋊Q8 | C2×D43 | semidirect |
| 110. #127 | C2×D43 | semidirect |
| 111. #124 | C2×D43 | semidirect |
| 174. C4 | #13063350 | semidirect |