Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
490 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 125 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×#13063322 | C2 | semidirect |
| 2. #14583289 | C2 | semidirect |
| 3. #14583265 | C2 | semidirect |
| 4. #14583099 | C2 | semidirect |
| 5. #14583094 | C2 | semidirect |
| 6. #14583049 | C2 | semidirect |
| 7. #14583032 | C2 | semidirect |
| 8. #14582956 | C2 | semidirect |
| 9. C43×#529 | C2 | semidirect |
| 13. C2×#10621884 | C22 | semidirect |
| 14. C2×#10621882 | C22 | semidirect |
| 19. C4⋊(C43⋊C8) | C22 | semidirect |
| 20. #13063245 | C22 | semidirect |
| 21. #13063245 | C22 | semidirect |
| 23. #13063236 | C22 | semidirect |
| 25. #125×C43 | C22 | semidirect |
| 26. #124×C43 | C22 | semidirect |
| 30. C4×Q8×C43 | C22 | semidirect |
| 32. C4×D4×C43 | C22 | semidirect |
| 129. #529 | D43 | semidirect |
| 137. C43 | #3217 | semidirect |
| 148. #125 | C2×D43 | semidirect |
| 149. #124 | C2×D43 | semidirect |
| 153. C4×Q8 | C2×D43 | semidirect |
| 155. C4×D4 | C2×D43 | semidirect |