Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
400 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 117 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×#13063344 | C2 | semidirect |
| 2. C2×D8×D43 | C2 | semidirect |
| 3. #14583333 | C2 | direct (N × H) |
| 4. C2×#13063270 | C2 | semidirect |
| 5. C2×#13063269 | C2 | semidirect |
| 6. C2×#13063266 | C2 | semidirect |
| 7. C2×#13063264 | C2 | semidirect |
| 8. C2×D16×C43 | C2 | semidirect |
| 12. #13063344 | C22 | semidirect |
| 13. C2×Dic172 | C22 | semidirect |
| 18. D8×D43 | C22 | semidirect |
| 20. #13063270 | C22 | semidirect |
| 21. #13063269 | C22 | semidirect |
| 22. #13063266 | C22 | semidirect |
| 23. #13063264 | C22 | semidirect |
| 24. C2×C43⋊C16 | C22 | semidirect |
| 26. C2×D8×C43 | C22 | semidirect |
| 27. D16×C43 | C22 | semidirect |
| 28. C2×C16×C43 | C22 | semidirect |
| 45. D8×C43 | C23 | semidirect |
| 51. Dic172 | C23 | semidirect |
| 56. C16×C43 | C23 | semidirect |
| 57. C43⋊C16 | C23 | semidirect |
| 100. C2×C43 | #509 | semidirect |
| 110. C2×D16 | D43 | semidirect |
| 112. C43 | C2×#509 | semidirect |
| 124. C2×D8 | C2×D43 | semidirect |
| 129. D16 | C2×D43 | semidirect |
| 132. C2×C16 | C2×D43 | semidirect |
| 155. D8 | C22×D43 | semidirect |
| 161. C16 | C22×D43 | semidirect |
| 205. C2 | #14583333 | direct (N × H) |