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. C23×D172 | C2 | semidirect |
| 3. C2×#13063353 | C2 | direct (N × H) |
| 4. C22×#10621873 | C2 | semidirect |
| 5. C22×D344 | C2 | semidirect |
| 6. C22×M16×C43 | C2 | semidirect |
| 9. C2×#10621898 | C22 | semidirect |
| 10. C22×Dic86 | C22 | semidirect |
| 14. C22×D172 | C22 | semidirect |
| 15. C22×D172 | C22 | semidirect |
| 18. #13063353 | C22 | direct (N × H) |
| 19. C2×#10621873 | C22 | semidirect |
| 20. C2×D344 | C22 | semidirect |
| 22. C2×M16×C43 | C22 | semidirect |
| 23. C22×C8×C43 | C22 | semidirect |
| 36. #10621898 | C23 | semidirect |
| 42. C2×D172 | C23 | semidirect |
| 43. C2×D172 | C23 | semidirect |
| 46. C2×Dic86 | C23 | semidirect |
| 47. M16×C43 | C23 | semidirect |
| 48. C2×C8×C43 | C23 | semidirect |
| 49. D344 | C23 | semidirect |
| 50. #10621873 | C23 | semidirect |
| 71. D172 | C24 | semidirect |
| 74. Dic86 | C24 | semidirect |
| 75. C8×C43 | C24 | semidirect |
| 77. C22×C43 | AGL(1,ℤ/8) | semidirect |
| 91. C2×C43 | C2×AGL(1,ℤ/8) | semidirect |
| 100. C22×M16 | D43 | semidirect |
| 101. C43 | C22×AGL(1,ℤ/8) | semidirect |
| 117. C2×M16 | C2×D43 | semidirect |
| 118. C22×C8 | C2×D43 | semidirect |
| 144. M16 | C22×D43 | semidirect |
| 145. C2×C8 | C22×D43 | semidirect |
| 170. C8 | C23×D43 | semidirect |
| 177. C22 | #13063353 | direct (N × H) |
| 187. C2 | C2×#13063353 | direct (N × H) |