Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1048 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1048 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 |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C22×#10621882 | C2 | semidirect |
| 3. #14583032 | C2 | direct (N × H) |
| 4. C2×#13063245 | C2 | semidirect |
| 5. C2×C22⋊(C43⋊C8) | C2 | semidirect |
| 6. C2×#121×C43 | C2 | semidirect |
| 12. C22×D172 | C22 | semidirect |
| 14. C2×#10621882 | C22 | semidirect |
| 15. C22×C43⋊C8 | C22 | semidirect |
| 16. #13063245 | C22 | semidirect |
| 17. C22⋊(C43⋊C8) | C22 | semidirect |
| 19. C22×D4×C43 | C22 | semidirect |
| 22. #121×C43 | C22 | semidirect |
| 23. C2×C4⋊C4×C43 | C22 | semidirect |
| 36. C2×D4×C43 | C23 | semidirect |
| 49. C2×D172 | D4 | semidirect |
| 52. C4⋊C4×C43 | C23 | semidirect |
| 56. C2×C43⋊C8 | C23 | semidirect |
| 63. C23×C43 | D8 | semidirect |
| 89. D172 | C2×D4 | semidirect |
| 100. C22×C43 | C2×D8 | semidirect |
| 115. C2×C43 | #447 | semidirect |
| 122. C2×#121 | D43 | semidirect |
| 126. C43 | C2×#447 | semidirect |
| 134. C22×D4 | C2×D43 | semidirect |
| 140. #121 | C2×D43 | semidirect |
| 141. C2×C4⋊C4 | C2×D43 | semidirect |
| 164. C2×D4 | C22×D43 | semidirect |
| 175. C4⋊C4 | C22×D43 | semidirect |
| 191. C23 | #10621882 | semidirect |
| 225. C22 | C2×#10621882 | semidirect |
| 235. C2 | #14583032 | direct (N × H) |