Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1504 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1504 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×#13063345 | C2 | direct (N × H) |
| 3. C22×#10621885 | C2 | semidirect |
| 4. C22×#10621883 | C2 | semidirect |
| 5. C22×#10621884 | C2 | semidirect |
| 6. C22×#10621882 | C2 | semidirect |
| 7. C23×C43⋊C8 | C2 | semidirect |
| 8. C22×#41×C43 | C2 | semidirect |
| 10. C2×#10621898 | C22 | semidirect |
| 15. #13063345 | C22 | direct (N × H) |
| 16. C2×#10621885 | C22 | semidirect |
| 17. C2×#10621883 | C22 | semidirect |
| 18. C2×#10621884 | C22 | semidirect |
| 19. C2×#10621882 | C22 | semidirect |
| 22. C22×C43⋊C8 | C22 | semidirect |
| 24. C2×#41×C43 | C22 | semidirect |
| 34. #41×C43 | C23 | semidirect |
| 49. #10621898 | C23 | semidirect |
| 55. #10621885 | C23 | semidirect |
| 56. #10621884 | C23 | semidirect |
| 57. #10621883 | C23 | semidirect |
| 58. #10621882 | C23 | semidirect |
| 61. C2×C43⋊C8 | C23 | semidirect |
| 93. C22×C43 | #135 | semidirect |
| 106. C2×C43 | C2×#135 | semidirect |
| 110. C22×#41 | D43 | semidirect |
| 117. C43 | C22×#135 | semidirect |
| 121. C2×#41 | C2×D43 | semidirect |
| 145. #41 | C22×D43 | semidirect |
| 204. C22 | #13063345 | direct (N × H) |
| 215. C2 | C2×#13063345 | direct (N × H) |