Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
448 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 448 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 |
|---|---|---|
| 2. #14583247 | C2 | semidirect |
| 3. #14583223 | C2 | semidirect |
| 4. #14583176 | C2 | semidirect |
| 5. #14583147 | C2 | semidirect |
| 6. #14583099 | C2 | semidirect |
| 7. #14583049 | C2 | semidirect |
| 8. C4×#10621884 | C2 | semidirect |
| 9. #14582977 | C2 | semidirect |
| 10. #14582903 | C2 | semidirect |
| 11. C43×#556 | C2 | semidirect |
| 15. C2×#10621884 | C22 | semidirect |
| 16. C2×#10621877 | C22 | semidirect |
| 22. #13063258 | C22 | semidirect |
| 23. #13063256 | C22 | semidirect |
| 24. C4⋊(C43⋊C8) | C22 | semidirect |
| 25. #13063249 | 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. C22⋊Q8×C43 | C22 | semidirect |
| 38. C4×Q8×C43 | C22 | semidirect |
| 40. #117×C43 | C22 | semidirect |
| 136. #556 | D43 | semidirect |
| 147. C43 | #3324 | semidirect |
| 153. C4⋊Q8 | C2×D43 | semidirect |
| 157. C22⋊Q8 | C2×D43 | semidirect |
| 162. C4×Q8 | C2×D43 | semidirect |
| 165. #117 | C2×D43 | semidirect |