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. C22×#10621898 | C2 | semidirect |
| 2. C2×#13063351 | C2 | direct (N × H) |
| 3. C22×#10621883 | C2 | semidirect |
| 4. C22×#10621882 | C2 | semidirect |
| 5. C22×#10621877 | C2 | semidirect |
| 6. C23×D4×C43 | C2 | semidirect |
| 8. C2×#10621898 | C22 | semidirect |
| 9. C22×Dic86 | C22 | semidirect |
| 10. C22×D172 | C22 | semidirect |
| 13. #13063351 | C22 | direct (N × H) |
| 14. C2×#10621883 | C22 | semidirect |
| 15. C2×#10621882 | C22 | semidirect |
| 16. C2×#10621877 | C22 | semidirect |
| 17. C22×C43⋊C8 | C22 | semidirect |
| 22. C22×D4×C43 | C22 | semidirect |
| 33. C2×D4×C43 | C23 | semidirect |
| 41. #10621898 | C23 | semidirect |
| 43. C2×D172 | C23 | semidirect |
| 46. C2×Dic86 | C23 | semidirect |
| 47. #10621883 | C23 | semidirect |
| 48. #10621882 | C23 | semidirect |
| 49. #10621877 | C23 | semidirect |
| 50. C2×C43⋊C8 | C23 | semidirect |
| 71. D172 | C24 | semidirect |
| 74. Dic86 | C24 | semidirect |
| 75. C43⋊C8 | C24 | semidirect |
| 80. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 92. C2×C43 | C2×AGL(1,ℤ/8) | semidirect |
| 96. C23×D4 | D43 | semidirect |
| 101. C43 | C22×AGL(1,ℤ/8) | semidirect |
| 111. C22×D4 | C2×D43 | semidirect |
| 135. C2×D4 | C22×D43 | semidirect |
| 177. C22 | #13063351 | direct (N × H) |
| 187. C2 | C2×#13063351 | direct (N × H) |