Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
556 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 556 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×#13063352 | C2 | semidirect |
| 2. #14583571 | C2 | semidirect |
| 3. D4×D172 | C2 | semidirect |
| 4. #14583276 | C2 | semidirect |
| 5. #14583153 | C2 | semidirect |
| 6. #14583099 | C2 | semidirect |
| 7. #14583094 | C2 | semidirect |
| 8. #14583047 | C2 | semidirect |
| 9. #14583034 | C2 | semidirect |
| 10. #14582978 | C2 | semidirect |
| 11. C4×SD16×C43 | C2 | semidirect |
| 12. C2×#10621902 | C22 | semidirect |
| 16. C2×#10621884 | C22 | semidirect |
| 17. C2×D344 | C22 | semidirect |
| 18. C2×D344 | C22 | semidirect |
| 20. C2×#10621872 | C22 | semidirect |
| 23. #13063322 | C22 | semidirect |
| 26. #13063300 | C22 | semidirect |
| 31. C4⋊(C43⋊C8) | C22 | semidirect |
| 32. #13063245 | C22 | semidirect |
| 33. #13063245 | C22 | semidirect |
| 34. (C2×D43)⋊C8 | C22 | semidirect |
| 36. C4×Q8×C43 | C22 | semidirect |
| 38. #106×C43 | C22 | semidirect |
| 39. #103×C43 | C22 | semidirect |
| 41. C4×C8×C43 | C22 | semidirect |
| 64. SD16×C43 | D4 | semidirect |
| 91. Q8×C43 | C2×D4 | semidirect |
| 119. C8×C43 | C2×D4 | semidirect |
| 139. C4×C43 | AGL(1,ℤ/8) | semidirect |
| 160. C4×SD16 | D43 | semidirect |
| 162. C43 | #3274 | semidirect |
| 181. C4×Q8 | C2×D43 | semidirect |
| 185. #106 | C2×D43 | semidirect |
| 187. #103 | C2×D43 | semidirect |
| 192. C4×C8 | C2×D43 | semidirect |
| 216. SD16 | D172 | semidirect |
| 242. Q8 | C2×D172 | semidirect |
| 271. C8 | C2×D172 | semidirect |
| 291. C4 | #13063352 | semidirect |