Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 806 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×#13063352 | C2 | semidirect |
| 3. #121×D43 | C2 | semidirect |
| 4. #14583047 | C2 | semidirect |
| 5. #14583043 | C2 | semidirect |
| 6. #14583038 | C2 | semidirect |
| 7. #14583035 | C2 | semidirect |
| 8. #14583032 | C2 | semidirect |
| 9. #14582899 | C2 | semidirect |
| 10. #14582861 | C2 | semidirect |
| 11. C43×#448 | C2 | semidirect |
| 16. C2×#10621902 | C22 | semidirect |
| 18. C22×D172 | C22 | semidirect |
| 20. C2×D4×D43 | C22 | semidirect |
| 24. C2×#10621884 | C22 | semidirect |
| 25. C2×D344 | C22 | semidirect |
| 26. C2×#10621882 | C22 | semidirect |
| 27. C2×#10621872 | C22 | semidirect |
| 28. #13063300 | C22 | semidirect |
| 32. #13063296 | C22 | semidirect |
| 33. C4⋊C4×D43 | C22 | semidirect |
| 35. #13063249 | C22 | semidirect |
| 36. #13063247 | C22 | semidirect |
| 37. #13063245 | C22 | semidirect |
| 38. C22⋊(C43⋊C8) | C22 | semidirect |
| 39. (C2×D43)⋊C8 | C22 | semidirect |
| 40. C22×Q8×C43 | C22 | semidirect |
| 41. C2×SD16×C43 | C22 | semidirect |
| 43. #103×C43 | C22 | semidirect |
| 44. C22⋊C8×C43 | C22 | semidirect |
| 64. #10621902 | D4 | semidirect |
| 115. Q8×C43 | C2×D4 | semidirect |
| 137. D172 | C2×D4 | semidirect |
| 152. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 192. #448 | D43 | semidirect |
| 197. C43 | #3006 | semidirect |
| 203. C22×Q8 | C2×D43 | semidirect |
| 212. C2×SD16 | C2×D43 | semidirect |
| 225. #103 | C2×D43 | semidirect |
| 230. C22⋊C8 | C2×D43 | semidirect |
| 301. Q8 | D4×D43 | semidirect |
| 353. C22 | #13063352 | semidirect |