Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
1424 conjugacy classes of subgroups; only the 545 normal subgroups are shown.
This group has 1424 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. #31771441 | C2 | semidirect |
| 2. #31771422 | C2 | semidirect |
| 3. #31771417 | C2 | semidirect |
| 4. #31771410 | C2 | semidirect |
| 5. #31771405 | C2 | semidirect |
| 6. C2×#22575475 | C2 | semidirect |
| 7. C2×#131×C269 | C2 | semidirect |
| 9. #22575500 | C22 | semidirect |
| 10. #22575499 | C22 | semidirect |
| 12. C2×#16864402 | C22 | semidirect |
| 14. #22575486 | C22 | semidirect |
| 15. #22575481 | C22 | semidirect |
| 16. #22575475 | C22 | semidirect |
| 17. #22575475 | C22 | semidirect |
| 18. #22575475 | C22 | semidirect |
| 19. #22575475 | C22 | semidirect |
| 20. C2×Dic1076 | C22 | semidirect |
| 21. C2×#16864391 | C22 | semidirect |
| 22. C2×D2152 | C22 | semidirect |
| 24. #131×C269 | C22 | semidirect |
| 25. #131×C269 | C22 | semidirect |
| 26. C2×M16×C269 | C22 | semidirect |
| 27. C22×C8×C269 | C22 | semidirect |
| 89. C269 | #3584 | semidirect |
| 97. C2×#131 | D269 | semidirect |
| 114. #131 | C2×D269 | semidirect |
| 115. #131 | C2×D269 | semidirect |
| 116. C2×M16 | C2×D269 | semidirect |
| 117. C22×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771441 | 2 |
| #31771422 | 2 |
| #31771417 | 2 |
| #31771410 | 2 |
| #31771405 | 2 |
| C2×#22575475 | 2 |
| C2×#131×C269 | 2 |
| #3584 | 269 |