Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
526 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575479 | C2 | semidirect |
| 2. C22×#16864387 | C2 | semidirect |
| 3. #31771174 | C2 | semidirect |
| 4. #31770820 | C2 | semidirect |
| 5. #31770800 | C2 | semidirect |
| 6. #31770632 | C2 | semidirect |
| 7. #31770609 | C2 | semidirect |
| 8. #31770599 | C2 | semidirect |
| 9. #518×C269 | C2 | semidirect |
| 13. C2×#16864390 | C22 | semidirect |
| 16. C2×#16864387 | C22 | semidirect |
| 19. #22575450 | C22 | semidirect |
| 20. #22575441 | C22 | semidirect |
| 23. C4⋊#14524130 | C22 | semidirect |
| 24. #22575376 | C22 | semidirect |
| 25. #22575373 | C22 | semidirect |
| 26. #22575373 | C22 | semidirect |
| 29. C4×D4×C269 | C22 | semidirect |
| 56. C2×D4×C269 | D4 | semidirect |
| 121. C269 | #3041 | semidirect |
| 126. #518 | D269 | semidirect |
| 147. C4×D4 | C2×D269 | semidirect |
| 169. C2×D4 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575479 | 2 |
| C22×#16864387 | 2 |
| #31771174 | 2 |
| #31770820 | 2 |
| #31770800 | 2 |
| #31770632 | 2 |
| #31770609 | 2 |
| #31770599 | 2 |
| #518×C269 | 2 |
| #3041 | 269 |