Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1008 conjugacy classes of subgroups; only the 229 normal subgroups are shown.
This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 229 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 |
|---|---|---|
| 2. C22×#10621872 | C2 | semidirect |
| 3. C2×#13063283 | C2 | semidirect |
| 4. #14582902 | C2 | direct (N × H) |
| 5. C2×#13063247 | C2 | semidirect |
| 6. C2×#13063246 | C2 | semidirect |
| 7. C2×#13063245 | C2 | semidirect |
| 8. C2×#102×C43 | C2 | semidirect |
| 14. C2×D4×D43 | C4 | semidirect |
| 18. C2×#10621872 | C22 | semidirect |
| 19. C22×C43⋊C8 | C22 | semidirect |
| 21. #13063283 | C22 | semidirect |
| 22. C2×C4⋊Dic43 | C22 | semidirect |
| 25. #13063247 | C22 | semidirect |
| 26. #13063246 | C22 | semidirect |
| 27. #13063245 | C22 | semidirect |
| 29. C22×C8×C43 | C22 | semidirect |
| 30. C2×C4⋊C4×C43 | C22 | semidirect |
| 31. #102×C43 | C22 | semidirect |
| 51. D4×D43 | C2×C4 | semidirect |
| 61. C2×C8×C43 | C23 | semidirect |
| 63. C4⋊C4×C43 | C23 | semidirect |
| 66. C4⋊Dic43 | C23 | semidirect |
| 69. C2×C43⋊C8 | C23 | semidirect |
| 135. C2×C43 | #418 | semidirect |
| 148. C2×#102 | D43 | semidirect |
| 149. C43 | C2×#418 | semidirect |
| 162. C22×C8 | C2×D43 | semidirect |
| 166. C2×C4⋊C4 | C2×D43 | semidirect |
| 172. #102 | C2×D43 | semidirect |
| 205. C2×C8 | C22×D43 | semidirect |
| 209. C4⋊C4 | C22×D43 | semidirect |
| 277. C2 | #14582902 | direct (N × H) |