Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
812 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 812 conjugacy classes of subgroups — too many to draw. Only its 165 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×#10621902 | C2 | semidirect |
| 2. C22×#10621882 | C2 | semidirect |
| 3. C2×#13063296 | C2 | semidirect |
| 4. #14583043 | C2 | direct (N × H) |
| 5. C2×#13063249 | C2 | semidirect |
| 6. C2×#13063247 | C2 | semidirect |
| 7. C2×(C2×D43)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C43 | C2 | semidirect |
| 12. C2×#10621902 | C22 | semidirect |
| 19. C2×#10621882 | C22 | semidirect |
| 22. #13063296 | C22 | semidirect |
| 25. #13063249 | C22 | semidirect |
| 26. #13063247 | C22 | semidirect |
| 27. (C2×D43)⋊C8 | C22 | semidirect |
| 31. C2×SD16×C43 | C22 | semidirect |
| 38. C2×Q8×C43 | D4 | semidirect |
| 57. C2×D172 | D4 | semidirect |
| 89. Q8×C43 | C2×D4 | semidirect |
| 107. D172 | C2×D4 | semidirect |
| 138. C2×C43 | #449 | semidirect |
| 145. C22×SD16 | D43 | semidirect |
| 152. C43 | C2×#449 | semidirect |
| 165. C2×SD16 | C2×D43 | semidirect |
| 185. C2×Q8 | C22⋊D43 | semidirect |
| 233. Q8 | C2×C22⋊D43 | semidirect |
| 283. C2 | #14583043 | direct (N × H) |