Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
546 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 546 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. C2×SD16×D43 | C2 | semidirect |
| 2. Q8×D172 | C2 | semidirect |
| 4. #14583272 | C2 | semidirect |
| 5. #14583129 | C2 | semidirect |
| 6. #14583104 | C2 | semidirect |
| 7. #14583099 | C2 | semidirect |
| 8. #14583051 | C2 | semidirect |
| 9. #14583039 | C2 | semidirect |
| 10. C8×D172 | C2 | semidirect |
| 11. C4×SD16×C43 | C2 | semidirect |
| 12. C2×Q8×D43 | C22 | semidirect |
| 15. C2×#10621873 | C22 | semidirect |
| 16. C2×#10621873 | C22 | semidirect |
| 18. C2×#10621884 | C22 | semidirect |
| 20. C2×C8×D43 | C22 | semidirect |
| 22. #13063325 | C22 | semidirect |
| 25. #13063305 | C22 | semidirect |
| 31. C4⋊(C43⋊C8) | C22 | semidirect |
| 32. #13063248 | 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 |
| 61. SD16×C43 | D4 | semidirect |
| 90. Q8×C43 | C2×D4 | semidirect |
| 108. D172 | SD16 | direct (N × H) |
| 116. C8×C43 | C2×D4 | semidirect |
| 128. C2×D43 | C2×SD16 | semidirect |
| 133. C4×C43 | C2×SD16 | semidirect |
| 154. C4×SD16 | D43 | semidirect |
| 156. C43 | D4×SD16 | semidirect |
| 175. C4×Q8 | C2×D43 | semidirect |
| 179. #106 | C2×D43 | semidirect |
| 182. #103 | C2×D43 | semidirect |
| 186. C4×C8 | C2×D43 | semidirect |
| 210. SD16 | D172 | direct (N × H) |
| 238. Q8 | C2×D172 | semidirect |
| 262. C8 | C2×D172 | semidirect |
| 280. C4 | SD16×D43 | semidirect |