Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1464 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1464 conjugacy classes of subgroups — too many to draw. Only its 545 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. #14583735 | C2 | semidirect |
| 2. #14583710 | C2 | semidirect |
| 3. #14583702 | C2 | semidirect |
| 4. #14583697 | C2 | semidirect |
| 5. C2×#13063351 | C2 | semidirect |
| 6. #14583666 | C2 | semidirect |
| 7. C2×H(5,𝔽2)×C43 | C2 | semidirect |
| 9. #13063372 | C22 | semidirect |
| 10. #13063371 | C22 | semidirect |
| 12. C2×#10621898 | C22 | semidirect |
| 14. #13063356 | C22 | semidirect |
| 15. #13063355 | C22 | semidirect |
| 16. #13063351 | C22 | semidirect |
| 17. #13063351 | C22 | semidirect |
| 18. #13063350 | C22 | semidirect |
| 19. #13063345 | C22 | semidirect |
| 20. C2×#10621883 | C22 | semidirect |
| 21. C2×#10621882 | C22 | semidirect |
| 22. #13063332 | C22 | semidirect |
| 23. C2×#10621877 | C22 | semidirect |
| 25. H(5,𝔽2)×C43 | C22 | semidirect |
| 28. C2×#41×C43 | C22 | semidirect |
| 30. C22×D4×C43 | C22 | semidirect |
| 56. #10621898 | C23 | semidirect |
| 57. C2×D172 | C23 | semidirect |
| 59. C2×Dic86 | C23 | semidirect |
| 60. #10621885 | C23 | semidirect |
| 61. #10621884 | C23 | semidirect |
| 62. #10621883 | C23 | semidirect |
| 63. #10621882 | C23 | semidirect |
| 65. #10621877 | C23 | semidirect |
| 66. C2×C43⋊C8 | C23 | semidirect |
| 116. C2×H(5,𝔽2) | D43 | semidirect |
| 122. C43 | #3585 | semidirect |
| 128. H(5,𝔽2) | C2×D43 | semidirect |
| 133. C2×#41 | C2×D43 | semidirect |
| 135. C22×D4 | C2×D43 | semidirect |