Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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. C22×#10621902 | C2 | semidirect |
| 2. C2×#13063348 | C2 | semidirect |
| 3. #14583412 | C2 | semidirect |
| 4. #14583060 | C2 | semidirect |
| 5. #14583049 | C2 | semidirect |
| 6. #14583047 | C2 | semidirect |
| 7. #14583038 | C2 | semidirect |
| 8. #14583035 | C2 | semidirect |
| 9. #14582894 | C2 | semidirect |
| 10. C22⋊C8×D43 | C2 | semidirect |
| 11. C43×#451 | C2 | semidirect |
| 17. C2×#10621902 | C22 | semidirect |
| 23. C2×#10621884 | C22 | semidirect |
| 24. C2×#10621884 | C22 | semidirect |
| 25. C2×D344 | C22 | semidirect |
| 26. C2×C8×D43 | C22 | semidirect |
| 28. #13063301 | C22 | semidirect |
| 29. #13063300 | C22 | semidirect |
| 34. #13063283 | C22 | semidirect |
| 35. #13063249 | C22 | semidirect |
| 36. #13063247 | C22 | semidirect |
| 37. #13063245 | C22 | semidirect |
| 39. (C2×D43)⋊C8 | C22 | semidirect |
| 41. C2×Q16×C43 | C22 | semidirect |
| 43. #103×C43 | C22 | semidirect |
| 61. #10621902 | D4 | semidirect |
| 143. C22×C43 | #135 | semidirect |
| 180. #451 | D43 | semidirect |
| 187. C43 | #3002 | semidirect |
| 200. C2×Q16 | C2×D43 | semidirect |
| 215. #103 | C2×D43 | semidirect |
| 333. C22 | #13063348 | semidirect |