Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
364 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 113 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. #135×D43 | C2 | semidirect |
| 2. #14583341 | C2 | semidirect |
| 3. #14583338 | C2 | semidirect |
| 4. #14583336 | C2 | semidirect |
| 5. #14583333 | C2 | semidirect |
| 6. #14583331 | C2 | semidirect |
| 7. #14583329 | C2 | semidirect |
| 8. C2×#13063264 | C2 | semidirect |
| 9. C43×#508 | C2 | semidirect |
| 12. #13063347 | C22 | semidirect |
| 16. Q16×D43 | C22 | semidirect |
| 18. D8×D43 | C22 | semidirect |
| 20. Dic344 | C22 | semidirect |
| 21. #13063271 | C22 | semidirect |
| 22. #13063270 | C22 | semidirect |
| 23. #13063269 | C22 | semidirect |
| 24. #13063268 | C22 | semidirect |
| 25. D688 | C22 | semidirect |
| 26. #13063266 | C22 | semidirect |
| 27. #13063264 | C22 | semidirect |
| 28. #13063264 | C22 | semidirect |
| 29. C2×C43⋊C16 | C22 | semidirect |
| 30. #135×C43 | C22 | semidirect |
| 31. Q32×C43 | C22 | semidirect |
| 32. SD32×C43 | C22 | semidirect |
| 33. D16×C43 | C22 | semidirect |
| 34. C2×C16×C43 | C22 | semidirect |
| 111. #508 | D43 | semidirect |
| 113. C43 | #3414 | semidirect |
| 120. #135 | C2×D43 | semidirect |
| 127. Q32 | C2×D43 | semidirect |
| 131. SD32 | C2×D43 | semidirect |
| 134. D16 | C2×D43 | semidirect |
| 138. C2×C16 | C2×D43 | semidirect |