Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#13063370 | C2 | semidirect |
| 2. C2×#13063351 | C2 | semidirect |
| 3. #14583066 | C2 | direct (N × H) |
| 4. C2×#13063253 | C2 | semidirect |
| 5. C2×#13063242 | C2 | semidirect |
| 6. C2×#127×C43 | C2 | semidirect |
| 9. #13063370 | C22 | semidirect |
| 15. #13063351 | C22 | semidirect |
| 18. C2×#10621877 | C22 | semidirect |
| 19. #13063253 | C22 | semidirect |
| 20. #13063242 | C22 | semidirect |
| 23. C22×D4×C43 | C22 | semidirect |
| 25. #127×C43 | C22 | semidirect |
| 26. C2×C42×C43 | C22 | semidirect |
| 39. C2×D4×C43 | C23 | semidirect |
| 53. #10621898 | D4 | semidirect |
| 55. C2×D172 | D4 | semidirect |
| 57. C2×Dic86 | D4 | semidirect |
| 59. C42×C43 | C23 | semidirect |
| 63. #10621877 | C23 | semidirect |
| 94. D172 | C2×D4 | semidirect |
| 98. Dic86 | C2×D4 | semidirect |
| 124. C2×C43 | #453 | semidirect |
| 129. C2×#127 | D43 | semidirect |
| 133. C43 | C2×#453 | semidirect |
| 143. C22×D4 | C2×D43 | semidirect |
| 150. #127 | C2×D43 | semidirect |
| 151. C2×C42 | C2×D43 | semidirect |
| 180. C2×D4 | C22×D43 | semidirect |
| 191. C42 | C22×D43 | semidirect |
| 251. C2 | #14583066 | direct (N × H) |