Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
5956 conjugacy classes of subgroups; only the 3205 normal subgroups are shown.
This group has 5956 conjugacy classes of subgroups — too many to draw. Only its 3205 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. #31771440 | C2 | direct (N × H) |
| 2. C2×#22575500 | C2 | semidirect |
| 3. C2×#22575498 | C2 | semidirect |
| 4. C22×#16864401 | C2 | semidirect |
| 5. C2×#41×D269 | C2 | semidirect |
| 6. C2×H(5,𝔽2)×C269 | C2 | semidirect |
| 7. #22575500 | C22 | semidirect |
| 8. #22575498 | C22 | semidirect |
| 9. C2×#16864403 | C22 | semidirect |
| 10. C2×#16864402 | C22 | semidirect |
| 11. C2×#16864401 | C22 | semidirect |
| 12. C2×#16864401 | C22 | semidirect |
| 13. C2×#16864401 | C22 | semidirect |
| 14. #41×D269 | C22 | semidirect |
| 15. C22×Dic538 | C22 | semidirect |
| 16. C2×Q8×D269 | C22 | semidirect |
| 17. C22×C22⋊D269 | C22 | semidirect |
| 18. C2×D4×D269 | C22 | semidirect |
| 19. C23×Dic269 | C22 | semidirect |
| 20. C22×C4×D269 | C22 | semidirect |
| 21. H(5,𝔽2)×C269 | C22 | semidirect |
| 22. C2×#41×C269 | C22 | semidirect |
| 23. C22×D4×C269 | C22 | semidirect |
| 25. #16864403 | C23 | semidirect |
| 26. #16864402 | C23 | semidirect |
| 27. #16864401 | C23 | semidirect |
| 28. #16864401 | C23 | semidirect |
| 30. C2×Dic538 | C23 | semidirect |
| 31. Q8×D269 | C23 | semidirect |
| 34. C2×C22⋊D269 | C23 | semidirect |
| 35. D4×D269 | C23 | semidirect |
| 38. C22×Dic269 | C23 | semidirect |
| 41. C2×C4×D269 | C23 | semidirect |
| 43. #41×C269 | C23 | semidirect |
| 46. C2×D4×C269 | C23 | semidirect |
| 78. C2×C269 | #585 | semidirect |
| 81. C269 | C2×#585 | semidirect |
| 86. C2×H(5,𝔽2) | D269 | semidirect |
| 91. H(5,𝔽2) | C2×D269 | semidirect |
| 98. C2×#41 | C2×D269 | semidirect |
| 103. C22×D4 | C2×D269 | semidirect |
| 112. #41 | C22×D269 | semidirect |
| 122. C2×D4 | C22×D269 | semidirect |
| 161. C2 | #31771440 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771440 | 2 |
| C2×#22575500 | 2 |
| C2×#22575498 | 2 |
| C22×#16864401 | 2 |
| C2×#41×D269 | 2 |
| C2×H(5,𝔽2)×C269 | 2 |
| C2×#585 | 269 |