Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
996 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 996 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 |
|---|---|---|
| 2. C22×#10621884 | C2 | semidirect |
| 3. C2×#13063301 | C2 | semidirect |
| 4. #14583048 | C2 | direct (N × H) |
| 5. C2×#13063247 | C2 | semidirect |
| 6. C2×#13063246 | C2 | semidirect |
| 7. C2×(C2×D43)⋊C8 | C2 | semidirect |
| 8. C22×SD16×C43 | C2 | semidirect |
| 18. C2×#10621884 | C22 | semidirect |
| 19. C22×C43⋊C8 | C22 | semidirect |
| 21. #13063301 | C22 | semidirect |
| 22. C2×C4⋊Dic43 | C22 | semidirect |
| 25. #13063247 | C22 | semidirect |
| 26. #13063246 | C22 | semidirect |
| 27. (C2×D43)⋊C8 | C22 | semidirect |
| 28. C22×Q8×C43 | C22 | semidirect |
| 31. C2×SD16×C43 | C22 | semidirect |
| 32. C22×C8×C43 | C22 | semidirect |
| 43. C2×Q8×C43 | C23 | semidirect |
| 67. C2×C8×C43 | C23 | semidirect |
| 71. C4⋊Dic43 | C23 | semidirect |
| 74. C2×C43⋊C8 | C23 | semidirect |
| 90. C22×D43 | SD16 | semidirect |
| 133. C2×D43 | C2×SD16 | semidirect |
| 142. C2×C43 | #450 | semidirect |
| 150. C22×SD16 | D43 | semidirect |
| 156. C43 | C2×#450 | semidirect |
| 158. C22×Q8 | C2×D43 | semidirect |
| 170. C2×SD16 | C2×D43 | semidirect |
| 172. C22×C8 | C2×D43 | semidirect |
| 191. C2×Q8 | C22×D43 | semidirect |
| 218. C2×C8 | C22×D43 | semidirect |
| 291. C2 | #14583048 | direct (N × H) |