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×#10621884 | C2 | semidirect |
| 3. #14583049 | C2 | direct (N × H) |
| 4. C2×#13063245 | C2 | semidirect |
| 5. C2×C22⋊(C43⋊C8) | C2 | semidirect |
| 6. C2×C22⋊Q8×C43 | C2 | semidirect |
| 14. C2×#10621884 | C22 | semidirect |
| 15. C22×C43⋊C8 | C22 | semidirect |
| 16. #13063245 | C22 | semidirect |
| 17. C22⋊(C43⋊C8) | C22 | semidirect |
| 18. C22×Q8×C43 | C22 | semidirect |
| 21. C22⋊Q8×C43 | C22 | semidirect |
| 23. C2×C4⋊C4×C43 | C22 | semidirect |
| 33. C2×Q8×C43 | C23 | semidirect |
| 51. C4⋊C4×C43 | C23 | semidirect |
| 55. C2×C43⋊C8 | C23 | semidirect |
| 58. C23×C43 | SD16 | semidirect |
| 92. C22×C43 | C2×SD16 | semidirect |
| 107. C2×C43 | #450 | semidirect |
| 114. C2×C22⋊Q8 | D43 | semidirect |
| 118. C43 | C2×#450 | semidirect |
| 120. C22×Q8 | C2×D43 | semidirect |
| 131. C22⋊Q8 | C2×D43 | semidirect |
| 133. C2×C4⋊C4 | C2×D43 | semidirect |
| 145. C2×Q8 | C22×D43 | semidirect |
| 166. C4⋊C4 | C22×D43 | semidirect |
| 178. C23 | #10621884 | semidirect |
| 209. C22 | C2×#10621884 | semidirect |
| 219. C2 | #14583049 | direct (N × H) |