Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
460 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 460 conjugacy classes of subgroups — too many to draw. Only its 123 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. D4×D172 | C2 | semidirect |
| 2. #14583247 | C2 | semidirect |
| 3. #14583223 | C2 | semidirect |
| 4. #14583186 | C2 | semidirect |
| 5. #14583150 | C2 | semidirect |
| 6. #14583094 | C2 | semidirect |
| 7. #14583032 | C2 | semidirect |
| 8. C4×#10621882 | C2 | semidirect |
| 9. #14582977 | C2 | semidirect |
| 10. #14582903 | C2 | semidirect |
| 11. C43×#555 | C2 | semidirect |
| 15. C2×#10621882 | C22 | semidirect |
| 16. C2×#10621877 | C22 | semidirect |
| 22. #13063258 | C22 | semidirect |
| 23. #13063256 | C22 | semidirect |
| 24. C4⋊(C43⋊C8) | C22 | semidirect |
| 25. #13063246 | C22 | semidirect |
| 28. #13063245 | C22 | semidirect |
| 29. #13063245 | C22 | semidirect |
| 30. #13063245 | C22 | semidirect |
| 31. C22⋊(C43⋊C8) | C22 | semidirect |
| 32. C4×C43⋊C8 | C22 | semidirect |
| 33. C4⋊Q8×C43 | C22 | semidirect |
| 36. #121×C43 | C22 | semidirect |
| 38. C4×D4×C43 | C22 | semidirect |
| 40. #117×C43 | C22 | semidirect |
| 141. #555 | D43 | semidirect |
| 152. C43 | #3325 | semidirect |
| 158. C4⋊Q8 | C2×D43 | semidirect |
| 164. #121 | C2×D43 | semidirect |
| 168. C4×D4 | C2×D43 | semidirect |
| 170. #117 | C2×D43 | semidirect |