Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 494 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 |
|---|---|---|
| 2. C22×#16864390 | C2 | semidirect |
| 3. #31771181 | C2 | semidirect |
| 4. #31770820 | C2 | semidirect |
| 5. #31770810 | C2 | semidirect |
| 6. #31770632 | C2 | semidirect |
| 7. #31770613 | C2 | semidirect |
| 8. #31770599 | C2 | semidirect |
| 9. #518×C269 | C2 | semidirect |
| 19. #22575453 | C22 | semidirect |
| 20. #22575441 | C22 | semidirect |
| 23. C4⋊#14524130 | C22 | semidirect |
| 24. #22575376 | C22 | semidirect |
| 25. #22575376 | C22 | semidirect |
| 26. #22575373 | C22 | semidirect |
| 116. C269 | #3042 | semidirect |
| 121. #518 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575479 | 2 |
| C22×#16864390 | 2 |
| #31771181 | 2 |
| #31770820 | 2 |
| #31770810 | 2 |
| #31770632 | 2 |
| #31770613 | 2 |
| #31770599 | 2 |
| #518×C269 | 2 |
| #3042 | 269 |