Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
728 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 728 conjugacy classes of subgroups — too many to draw. Only its 165 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×#13063350 | C2 | semidirect |
| 2. C2×#13063314 | C2 | semidirect |
| 3. #14583072 | C2 | direct (N × H) |
| 4. C2×#13063252 | C2 | semidirect |
| 5. C2×#13063244 | C2 | semidirect |
| 6. C2×2−1+4×C43 | C2 | semidirect |
| 9. #13063350 | C22 | semidirect |
| 14. #13063314 | C22 | semidirect |
| 17. #13063252 | C22 | semidirect |
| 18. #13063244 | C22 | semidirect |
| 21. 2−1+4×C43 | C22 | semidirect |
| 115. C2×C43 | #454 | semidirect |
| 118. C2×2−1+4 | D43 | semidirect |
| 124. C43 | C2×#454 | semidirect |
| 127. 2−1+4 | C2×D43 | semidirect |
| 233. C2 | #14583072 | direct (N × H) |