Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1018 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 1018 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×#13063370 | C2 | semidirect |
| 2. C2×#13063295 | C2 | semidirect |
| 3. C2×#13063293 | C2 | semidirect |
| 4. #14583087 | C2 | direct (N × H) |
| 5. C2×#13063239 | C2 | semidirect |
| 6. C2×#99×C43 | C2 | semidirect |
| 7. C24×D43 | C22 | semidirect |
| 10. #13063370 | C22 | semidirect |
| 19. #13063295 | C22 | semidirect |
| 21. #13063293 | C22 | semidirect |
| 22. C2×C22⋊Dic43 | C22 | semidirect |
| 25. #13063239 | C22 | semidirect |
| 27. C2×C22⋊C4×C43 | C22 | semidirect |
| 28. #99×C43 | C22 | semidirect |
| 29. C24×C43 | D4 | semidirect |
| 37. C23×D43 | D4 | semidirect |
| 38. C23×D43 | C23 | semidirect |
| 41. C2×D4×C43 | D4 | semidirect |
| 44. C22×C4×C43 | D4 | semidirect |
| 54. C2×C22⋊D43 | D4 | semidirect |
| 58. C22×Dic43 | D4 | semidirect |
| 71. C22⋊C4×C43 | C23 | semidirect |
| 73. C22⋊Dic43 | C23 | semidirect |
| 84. C23×C43 | C2×D4 | semidirect |
| 103. C22×D43 | C2×D4 | semidirect |
| 110. C2×C4×C43 | C2×D4 | semidirect |
| 122. C2×Dic43 | C2×D4 | semidirect |
| 164. C2×C43 | B(4,𝔽2) | semidirect |
| 173. C2×#99 | D43 | semidirect |
| 174. C43 | C2×B(4,𝔽2) | semidirect |
| 194. C2×C22⋊C4 | C2×D43 | semidirect |
| 196. #99 | C2×D43 | semidirect |
| 205. C24 | D172 | semidirect |
| 230. C2×D4 | D172 | semidirect |
| 237. C22×C4 | D172 | semidirect |
| 243. C22⋊C4 | C22×D43 | semidirect |
| 268. C23 | C2×D172 | semidirect |
| 294. C2×C4 | C2×D172 | semidirect |
| 333. C2 | #14583087 | direct (N × H) |