Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
728 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063372 | C2 | semidirect |
| 2. C2×#13063353 | C2 | semidirect |
| 3. C2×#13063350 | C2 | semidirect |
| 4. C2×#13063313 | C2 | semidirect |
| 5. #14583073 | C2 | direct (N × H) |
| 6. C2×#13063253 | C2 | semidirect |
| 7. C2×#13063243 | C2 | semidirect |
| 8. C2×#104×C43 | C2 | semidirect |
| 12. #13063372 | C22 | semidirect |
| 22. #13063353 | C22 | semidirect |
| 24. #13063350 | C22 | semidirect |
| 31. #13063313 | C22 | semidirect |
| 33. #13063253 | C22 | semidirect |
| 34. #13063243 | C22 | semidirect |
| 38. #104×C43 | C22 | semidirect |
| 172. C2×C43 | #454 | semidirect |
| 182. C2×#104 | D43 | semidirect |
| 184. C43 | C2×#454 | semidirect |
| 213. #104 | C2×D43 | semidirect |
| 349. C2 | #14583073 | direct (N × H) |