Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1512 conjugacy classes of subgroups; only the 549 normal subgroups are shown.
This group has 1512 conjugacy classes of subgroups — too many to draw. Only its 549 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. C2×#13063371 | C2 | semidirect |
| 2. #14583704 | C2 | direct (N × H) |
| 3. C2×#13063353 | C2 | semidirect |
| 4. C2×#13063347 | C2 | semidirect |
| 5. C22×D344 | C2 | semidirect |
| 6. C2×#131×C43 | C2 | semidirect |
| 8. #13063371 | C22 | semidirect |
| 10. C2×#10621898 | C22 | semidirect |
| 11. C22×D172 | C22 | semidirect |
| 13. #13063353 | C22 | semidirect |
| 14. #13063347 | C22 | semidirect |
| 15. C2×Dic172 | C22 | semidirect |
| 16. C2×#10621873 | C22 | semidirect |
| 17. C2×D344 | C22 | semidirect |
| 18. C2×D344 | C22 | semidirect |
| 19. C2×D344 | C22 | semidirect |
| 21. #131×C43 | C22 | semidirect |
| 22. C2×M16×C43 | C22 | semidirect |
| 23. C22×C8×C43 | C22 | semidirect |
| 34. #10621898 | C23 | semidirect |
| 38. C2×D172 | C23 | semidirect |
| 41. M16×C43 | C23 | semidirect |
| 44. C2×C8×C43 | C23 | semidirect |
| 45. Dic172 | C23 | semidirect |
| 46. D344 | C23 | semidirect |
| 47. D344 | C23 | semidirect |
| 48. #10621873 | C23 | semidirect |
| 81. C2×C43 | #576 | semidirect |
| 89. C2×#131 | D43 | semidirect |
| 90. C43 | C2×#576 | semidirect |
| 105. #131 | C2×D43 | semidirect |
| 106. C2×M16 | C2×D43 | semidirect |
| 107. C22×C8 | C2×D43 | semidirect |
| 129. M16 | C22×D43 | semidirect |
| 132. C2×C8 | C22×D43 | semidirect |
| 165. C2 | #14583704 | direct (N × H) |