Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
492 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 492 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. #14583444 | C2 | semidirect |
| 2. C2×#13063287 | C2 | semidirect |
| 3. #14583212 | C2 | semidirect |
| 4. #14583178 | C2 | semidirect |
| 5. #14583093 | C2 | semidirect |
| 6. #14583035 | C2 | semidirect |
| 7. #14583032 | C2 | semidirect |
| 8. #14582981 | C2 | semidirect |
| 9. #14582979 | C2 | semidirect |
| 10. #14582949 | C2 | semidirect |
| 11. C43×#480 | C2 | semidirect |
| 17. #13063324 | C22 | semidirect |
| 18. #13063321 | C22 | semidirect |
| 22. D4×Dic43 | C22 | semidirect |
| 27. #13063287 | C22 | semidirect |
| 31. #13063258 | C22 | semidirect |
| 32. Dic43⋊C8 | C22 | semidirect |
| 35. #13063245 | C22 | semidirect |
| 37. C8×Dic43 | C22 | semidirect |
| 40. #107×C43 | C22 | semidirect |
| 41. #102×C43 | C22 | semidirect |
| 104. C2×Dic43 | D8 | semidirect |
| 112. D172 | #41 | semidirect |
| 153. #480 | D43 | semidirect |
| 161. C43 | #3100 | semidirect |
| 184. #107 | C2×D43 | semidirect |
| 189. #102 | C2×D43 | semidirect |