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. C2×#22575478 | C2 | semidirect |
| 2. C2×#22575478 | C2 | semidirect |
| 3. #31771372 | C2 | semidirect |
| 4. #31770873 | C2 | semidirect |
| 5. #31770870 | C2 | semidirect |
| 6. #31770653 | C2 | semidirect |
| 7. #31770589 | C2 | semidirect |
| 8. C2×#22575369 | C2 | semidirect |
| 9. #575×C269 | C2 | semidirect |
| 16. C2×#16864389 | C22 | semidirect |
| 18. C2×#16864387 | C22 | semidirect |
| 20. #22575460 | C22 | semidirect |
| 25. #22575388 | C22 | semidirect |
| 26. #22575372 | C22 | semidirect |
| 27. #22575370 | C22 | semidirect |
| 28. #22575369 | C22 | semidirect |
| 32. #137×C269 | C22 | semidirect |
| 34. AGL(1,ℤ/8)×C269 | C22 | semidirect |
| 147. C269 | #3068 | semidirect |
| 149. #575 | D269 | semidirect |
| 162. #137 | C2×D269 | semidirect |
| 168. AGL(1,ℤ/8) | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575478 | 2 |
| #31771372 | 2 |
| #31770873 | 2 |
| #31770870 | 2 |
| #31770653 | 2 |
| #31770589 | 2 |
| C2×#22575369 | 2 |
| #575×C269 | 2 |
| #3068 | 269 |