Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31771403 | C2 | semidirect |
| 2. C2×#22575479 | C2 | semidirect |
| 3. #31771372 | C2 | semidirect |
| 4. #31770873 | C2 | semidirect |
| 5. #31770866 | C2 | semidirect |
| 6. #31770653 | C2 | semidirect |
| 7. #31770587 | C2 | semidirect |
| 8. C2×#22575370 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C269 | C2 | semidirect |
| 12. #22575483 | C22 | semidirect |
| 16. #22575478 | C22 | semidirect |
| 18. C2×#16864390 | C22 | semidirect |
| 19. C2×#16864387 | C22 | semidirect |
| 21. #22575460 | C22 | semidirect |
| 26. #22575388 | C22 | semidirect |
| 27. #22575371 | C22 | semidirect |
| 28. #22575370 | C22 | semidirect |
| 29. #22575369 | C22 | semidirect |
| 147. C269 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771403 | 2 |
| C2×#22575479 | 2 |
| #31771372 | 2 |
| #31770873 | 2 |
| #31770866 | 2 |
| #31770653 | 2 |
| #31770587 | 2 |
| C2×#22575370 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #3068 | 269 |