Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
738 conjugacy classes of subgroups; only the 289 normal subgroups are shown.
This group has 738 conjugacy classes of subgroups — too many to draw. Only its 289 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. #14583666 | C2 | semidirect |
| 2. #41×Dic43 | C2 | semidirect |
| 3. #14582916 | C2 | semidirect |
| 4. C2×#13063252 | C2 | semidirect |
| 7. C2×#10621877 | C22 | semidirect |
| 10. #13063284 | C22 | semidirect |
| 11. C2×C4×Dic43 | C22 | semidirect |
| 12. #13063252 | C22 | semidirect |
| 13. #13063252 | C22 | semidirect |
| 15. 2−1+4×C43 | C4 | semidirect |
| 17. H(5,𝔽2)×C43 | C4 | semidirect |
| 26. #41×C43 | C2×C4 | semidirect |
| 30. C2×Q8×C43 | C2×C4 | semidirect |
| 34. C2×D4×C43 | C2×C4 | semidirect |
| 89. C43 | #2901 | semidirect |
| 91. 2−1+4 | Dic43 | semidirect |
| 93. H(5,𝔽2) | Dic43 | semidirect |
| 110. #41 | C2×Dic43 | semidirect |
| 114. C2×Q8 | C2×Dic43 | semidirect |
| 118. C2×D4 | C2×Dic43 | semidirect |