Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
420 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 117 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. #14583468 | C2 | semidirect |
| 2. #14583286 | C2 | semidirect |
| 3. #14583275 | C2 | semidirect |
| 4. #14583265 | C2 | semidirect |
| 5. #14583256 | C2 | semidirect |
| 6. #14583114 | C2 | semidirect |
| 7. #14583094 | C2 | semidirect |
| 8. #14583042 | C2 | semidirect |
| 9. #14583032 | C2 | semidirect |
| 10. #14582960 | C2 | semidirect |
| 11. C43×#540 | C2 | semidirect |
| 14. C2×#10621883 | C22 | semidirect |
| 17. C2×#10621882 | C22 | semidirect |
| 24. C4⋊(C43⋊C8) | C22 | semidirect |
| 25. #13063248 | C22 | semidirect |
| 28. #13063245 | C22 | semidirect |
| 30. #13063236 | C22 | semidirect |
| 31. C4×C43⋊C8 | C22 | semidirect |
| 32. #127×C43 | C22 | semidirect |
| 33. #125×C43 | C22 | semidirect |
| 37. C4×D4×C43 | C22 | semidirect |
| 129. #540 | D43 | semidirect |
| 140. C43 | #3220 | semidirect |
| 149. #127 | C2×D43 | semidirect |
| 150. #125 | C2×D43 | semidirect |
| 158. C4×D4 | C2×D43 | semidirect |