Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
996 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 996 conjugacy classes of subgroups — too many to draw. Only its 181 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×#10621873 | C2 | semidirect |
| 3. C2×#13063304 | C2 | semidirect |
| 4. #14583052 | C2 | direct (N × H) |
| 5. C2×#13063247 | C2 | semidirect |
| 6. C2×C22⋊C8×C43 | C2 | semidirect |
| 8. C22×Dic86 | C22 | semidirect |
| 15. C2×#10621873 | C22 | semidirect |
| 17. #13063304 | C22 | semidirect |
| 18. C2×C4⋊Dic43 | C22 | semidirect |
| 21. #13063247 | C22 | semidirect |
| 23. C22×C8×C43 | C22 | semidirect |
| 24. C22⋊C8×C43 | C22 | semidirect |
| 48. C2×Dic86 | C23 | semidirect |
| 50. C2×C8×C43 | C23 | semidirect |
| 53. C4⋊Dic43 | C23 | semidirect |
| 58. C23×C43 | SD16 | semidirect |
| 92. C22×C43 | C2×SD16 | semidirect |
| 107. C2×C43 | #450 | semidirect |
| 117. C2×C22⋊C8 | D43 | semidirect |
| 118. C43 | C2×#450 | semidirect |
| 129. C22×C8 | C2×D43 | semidirect |
| 136. C22⋊C8 | C2×D43 | semidirect |
| 163. C2×C8 | C22×D43 | semidirect |
| 178. C23 | #10621873 | semidirect |
| 209. C22 | C2×#10621873 | semidirect |
| 219. C2 | #14583052 | direct (N × H) |