Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
764 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 764 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063371 | C2 | semidirect |
| 2. C2×#13063353 | C2 | semidirect |
| 3. C2×#13063345 | C2 | semidirect |
| 4. #14583480 | C2 | semidirect |
| 5. #14583064 | C2 | semidirect |
| 6. #14583051 | C2 | semidirect |
| 7. #14583047 | C2 | semidirect |
| 8. #14583034 | C2 | semidirect |
| 9. C2×#13063245 | C2 | semidirect |
| 10. #14582867 | C2 | semidirect |
| 11. C43×#417 | C2 | semidirect |
| 17. C2×#10621898 | C22 | semidirect |
| 24. C2×#10621885 | C22 | semidirect |
| 25. C2×#10621873 | C22 | semidirect |
| 26. C2×#10621883 | C22 | semidirect |
| 27. C2×#10621884 | C22 | semidirect |
| 28. C2×D344 | C22 | semidirect |
| 29. C2×#10621882 | C22 | semidirect |
| 30. C22×C43⋊C8 | C22 | semidirect |
| 32. #13063305 | C22 | semidirect |
| 34. #13063300 | C22 | semidirect |
| 36. #13063245 | C22 | semidirect |
| 37. #13063245 | C22 | semidirect |
| 38. (C2×D43)⋊C8 | C22 | semidirect |
| 39. (C2×D43)⋊C8 | C22 | semidirect |
| 41. C2×M16×C43 | C22 | semidirect |
| 42. C2×C4⋊C4×C43 | C22 | semidirect |
| 43. #103×C43 | C22 | semidirect |
| 44. #102×C43 | C22 | semidirect |
| 48. #41×C43 | D4 | semidirect |
| 74. C2×D172 | D4 | semidirect |
| 187. #417 | D43 | semidirect |
| 190. C43 | #3012 | semidirect |
| 210. C2×M16 | C2×D43 | semidirect |
| 217. C2×C4⋊C4 | C2×D43 | semidirect |
| 218. #103 | C2×D43 | semidirect |
| 221. #102 | C2×D43 | semidirect |
| 234. #41 | D172 | semidirect |