Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1720 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1720 conjugacy classes of subgroups — too many to draw. Only its 565 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. C2×#13063350 | C2 | direct (N × H) |
| 3. C22×#10621884 | C2 | semidirect |
| 4. C22×#10621882 | C2 | semidirect |
| 5. C22×#10621877 | C2 | semidirect |
| 6. C22×#41×C43 | C2 | semidirect |
| 11. C22×D172 | C22 | semidirect |
| 12. #13063350 | C22 | direct (N × H) |
| 13. C2×#10621884 | C22 | semidirect |
| 14. C2×#10621882 | C22 | semidirect |
| 15. C2×#10621877 | C22 | semidirect |
| 16. C22×C43⋊C8 | C22 | semidirect |
| 18. C2×#41×C43 | C22 | semidirect |
| 19. C22×Q8×C43 | C22 | semidirect |
| 21. C22×D4×C43 | C22 | semidirect |
| 30. #41×C43 | C23 | semidirect |
| 32. C2×Q8×C43 | C23 | semidirect |
| 35. C2×D4×C43 | C23 | semidirect |
| 46. C2×D172 | C23 | semidirect |
| 47. #10621884 | C23 | semidirect |
| 48. #10621882 | C23 | semidirect |
| 49. #10621877 | C23 | semidirect |
| 50. C2×C43⋊C8 | C23 | semidirect |
| 61. Q8×C43 | C24 | semidirect |
| 64. D4×C43 | C24 | semidirect |
| 75. C43⋊C8 | C24 | semidirect |
| 79. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 92. C2×C43 | C2×AGL(1,ℤ/8) | semidirect |
| 95. C22×#41 | D43 | semidirect |
| 101. C43 | C22×AGL(1,ℤ/8) | semidirect |
| 104. C2×#41 | C2×D43 | semidirect |
| 105. C22×Q8 | C2×D43 | semidirect |
| 111. C22×D4 | C2×D43 | semidirect |
| 125. #41 | C22×D43 | semidirect |
| 127. C2×Q8 | C22×D43 | semidirect |
| 135. C2×D4 | C22×D43 | semidirect |
| 156. Q8 | C23×D43 | semidirect |
| 162. D4 | C23×D43 | semidirect |
| 177. C22 | #13063350 | direct (N × H) |
| 187. C2 | C2×#13063350 | direct (N × H) |