Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
370 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 113 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. #14583701 | C2 | semidirect |
| 2. #14583336 | C2 | semidirect |
| 3. #14583334 | C2 | semidirect |
| 4. #14583332 | C2 | semidirect |
| 5. C2×D688 | C2 | semidirect |
| 6. D16×D43 | C2 | semidirect |
| 7. #14583315 | C2 | semidirect |
| 8. C43×#508 | C2 | semidirect |
| 12. #13063348 | C22 | semidirect |
| 13. C2×D344 | C22 | semidirect |
| 14. D8×D43 | C22 | semidirect |
| 16. #13063268 | C22 | semidirect |
| 17. D688 | C22 | semidirect |
| 18. D688 | C22 | semidirect |
| 19. #13063266 | C22 | semidirect |
| 20. #13063265 | C22 | semidirect |
| 21. #13063264 | C22 | semidirect |
| 22. C16×D43 | C22 | semidirect |
| 23. #135×C43 | C22 | semidirect |
| 24. Q32×C43 | C22 | semidirect |
| 25. SD32×C43 | C22 | semidirect |
| 26. D16×C43 | C22 | semidirect |
| 27. C2×C16×C43 | C22 | semidirect |
| 89. #508 | D43 | semidirect |
| 93. C43 | #3415 | semidirect |
| 98. #135 | C2×D43 | semidirect |
| 102. Q32 | C2×D43 | semidirect |
| 104. SD32 | C2×D43 | semidirect |
| 108. D16 | C2×D43 | semidirect |
| 112. C2×C16 | C2×D43 | semidirect |