Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
736 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 736 conjugacy classes of subgroups — too many to draw. Only its 161 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. #14583463 | C2 | semidirect |
| 3. #14583072 | C2 | semidirect |
| 4. #14583067 | C2 | semidirect |
| 5. #14582916 | C2 | semidirect |
| 6. #14582883 | C2 | semidirect |
| 7. C43×#585 | C2 | semidirect |
| 8. C22×D172 | C22 | semidirect |
| 10. #13063350 | C22 | semidirect |
| 13. C2×#10621877 | C22 | semidirect |
| 14. #13063321 | C22 | semidirect |
| 15. #13063314 | C22 | semidirect |
| 18. #13063284 | C22 | semidirect |
| 19. #13063252 | C22 | semidirect |
| 20. #13063244 | C22 | semidirect |
| 21. #13063242 | C22 | semidirect |
| 23. 2−1+4×C43 | C22 | semidirect |
| 26. H(5,𝔽2)×C43 | C22 | semidirect |
| 42. #41×C43 | D4 | semidirect |
| 46. C2×Q8×C43 | D4 | semidirect |
| 54. C2×D4×C43 | D4 | semidirect |
| 135. #585 | D43 | semidirect |
| 142. C43 | #3021 | semidirect |
| 144. 2−1+4 | C2×D43 | semidirect |
| 147. H(5,𝔽2) | C2×D43 | semidirect |
| 177. #41 | C22⋊D43 | semidirect |
| 181. C2×Q8 | C22⋊D43 | semidirect |
| 194. C2×D4 | C22⋊D43 | semidirect |