Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
616 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#10621882 | C2 | semidirect |
| 2. C23×C43⋊C8 | C2 | semidirect |
| 3. C2×#13063299 | C2 | semidirect |
| 4. #14583133 | C2 | direct (N × H) |
| 5. C2×#13063258 | C2 | semidirect |
| 6. C2×#13063246 | C2 | semidirect |
| 7. C2×#13063245 | C2 | semidirect |
| 8. C2×#121×C43 | C2 | semidirect |
| 12. C2×#10621882 | C22 | semidirect |
| 16. C22×C43⋊C8 | C22 | semidirect |
| 18. #13063299 | C22 | semidirect |
| 21. #13063258 | C22 | semidirect |
| 22. #13063246 | C22 | semidirect |
| 23. #13063245 | C22 | semidirect |
| 28. #121×C43 | C22 | semidirect |
| 63. C2×C43⋊C8 | D4 | semidirect |
| 72. C23×C43 | D8 | semidirect |
| 101. C43⋊C8 | C2×D4 | semidirect |
| 111. C22×C43 | C2×D8 | semidirect |
| 127. C2×C43 | #466 | semidirect |
| 135. C2×#121 | D43 | semidirect |
| 140. C43 | C2×#466 | semidirect |
| 155. #121 | C2×D43 | semidirect |
| 208. C23 | #10621882 | semidirect |
| 247. C22 | C2×#10621882 | semidirect |
| 259. C2 | #14583133 | direct (N × H) |