Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
546 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 546 conjugacy classes of subgroups — too many to draw. Only its 133 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×#13063349 | C2 | semidirect |
| 2. #14583553 | C2 | semidirect |
| 3. D4×D172 | C2 | semidirect |
| 4. #14583272 | C2 | semidirect |
| 5. #14583146 | C2 | semidirect |
| 6. #14583104 | C2 | semidirect |
| 7. #14583094 | C2 | semidirect |
| 8. #14583051 | C2 | semidirect |
| 9. #14583045 | C2 | semidirect |
| 10. #14582978 | C2 | semidirect |
| 11. C4×D8×C43 | C2 | semidirect |
| 12. C2×#10621900 | C22 | semidirect |
| 16. C2×#10621873 | C22 | semidirect |
| 17. C2×#10621873 | C22 | semidirect |
| 19. C2×#10621882 | C22 | semidirect |
| 20. C2×#10621872 | C22 | semidirect |
| 21. #13063325 | C22 | semidirect |
| 24. #13063305 | C22 | semidirect |
| 31. C4⋊(C43⋊C8) | C22 | semidirect |
| 32. #13063248 | C22 | semidirect |
| 33. #13063245 | C22 | semidirect |
| 34. (C2×D43)⋊C8 | C22 | semidirect |
| 37. C4×D4×C43 | C22 | semidirect |
| 38. #107×C43 | C22 | semidirect |
| 40. #102×C43 | C22 | semidirect |
| 41. C4×C8×C43 | C22 | semidirect |
| 62. D8×C43 | D4 | semidirect |
| 93. D4×C43 | C2×D4 | semidirect |
| 117. C8×C43 | C2×D4 | semidirect |
| 136. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 158. C4×D8 | D43 | semidirect |
| 160. C43 | #3272 | semidirect |
| 181. C4×D4 | C2×D43 | semidirect |
| 183. #107 | C2×D43 | semidirect |
| 188. #102 | C2×D43 | semidirect |
| 190. C4×C8 | C2×D43 | semidirect |
| 215. D8 | D172 | semidirect |
| 252. D4 | C2×D172 | semidirect |
| 267. C8 | C2×D172 | semidirect |
| 287. C4 | #13063349 | semidirect |