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. C2×#13063348 | C2 | semidirect |
| 2. #135×D43 | C2 | semidirect |
| 3. #14583341 | C2 | semidirect |
| 4. #14583340 | C2 | semidirect |
| 5. #14583337 | C2 | semidirect |
| 6. #14583336 | C2 | semidirect |
| 7. #14583334 | C2 | semidirect |
| 8. #14583332 | C2 | semidirect |
| 9. #14583330 | C2 | semidirect |
| 10. M32×D43 | C2 | semidirect |
| 11. C43×#510 | C2 | semidirect |
| 17. #13063348 | C22 | semidirect |
| 18. #13063348 | C22 | semidirect |
| 22. #13063344 | C22 | semidirect |
| 23. Q16×D43 | C22 | semidirect |
| 26. C2×D344 | C22 | semidirect |
| 27. D8×D43 | C22 | semidirect |
| 29. #13063271 | C22 | semidirect |
| 30. #13063270 | C22 | semidirect |
| 31. #13063268 | C22 | semidirect |
| 32. #13063268 | C22 | semidirect |
| 33. D688 | C22 | semidirect |
| 34. #13063266 | C22 | semidirect |
| 35. #13063265 | C22 | semidirect |
| 36. #13063264 | C22 | semidirect |
| 37. C16×D43 | C22 | semidirect |
| 39. C2×Q16×C43 | C22 | semidirect |
| 40. Q32×C43 | C22 | semidirect |
| 41. SD32×C43 | C22 | semidirect |
| 42. M32×C43 | C22 | semidirect |
| 151. #510 | D43 | semidirect |
| 158. C43 | #3414 | semidirect |
| 172. C2×Q16 | C2×D43 | semidirect |
| 179. Q32 | C2×D43 | semidirect |
| 183. SD32 | C2×D43 | semidirect |
| 188. M32 | C2×D43 | semidirect |