Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
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. #31771406 | C2 | semidirect |
| 2. #31771041 | C2 | semidirect |
| 3. #31771039 | C2 | semidirect |
| 4. #31771037 | C2 | semidirect |
| 5. #31771034 | C2 | semidirect |
| 6. D16×D269 | C2 | semidirect |
| 7. #31771021 | C2 | semidirect |
| 8. C2×D16×C269 | C2 | semidirect |
| 12. #22575475 | C22 | semidirect |
| 13. #22575472 | C22 | semidirect |
| 14. D8×D269 | C22 | semidirect |
| 16. Dic2152 | C22 | semidirect |
| 17. #22575398 | C22 | semidirect |
| 18. #22575397 | C22 | semidirect |
| 19. D4304 | C22 | semidirect |
| 20. #22575394 | C22 | semidirect |
| 21. #22575393 | C22 | semidirect |
| 22. #22575392 | C22 | semidirect |
| 23. C16×D269 | C22 | semidirect |
| 24. C2×D8×C269 | C22 | semidirect |
| 25. D16×C269 | C22 | semidirect |
| 26. D16×C269 | C22 | semidirect |
| 27. C2×C16×C269 | C22 | semidirect |
| 84. C269 | #3415 | semidirect |
| 92. C2×D16 | D269 | semidirect |
| 100. C2×D8 | C2×D269 | semidirect |
| 107. D16 | C2×D269 | semidirect |
| 108. D16 | C2×D269 | semidirect |
| 112. C2×C16 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771406 | 2 |
| #31771041 | 2 |
| #31771039 | 2 |
| #31771037 | 2 |
| #31771034 | 2 |
| D16×D269 | 2 |
| #31771021 | 2 |
| C2×D16×C269 | 2 |
| #3415 | 269 |