Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31770971 | C2 | semidirect |
| 3. #31770967 | C2 | semidirect |
| 4. #31770962 | C2 | semidirect |
| 5. #31770953 | C2 | semidirect |
| 6. #31770609 | C2 | semidirect |
| 7. #31770604 | C2 | semidirect |
| 8. #31770599 | C2 | semidirect |
| 9. C2×#22575373 | C2 | semidirect |
| 10. #31770561 | C2 | semidirect |
| 11. #544×C269 | C2 | semidirect |
| 21. #22575376 | C22 | semidirect |
| 22. #22575376 | C22 | semidirect |
| 23. #22575376 | C22 | semidirect |
| 28. #22575373 | C22 | semidirect |
| 29. #22575373 | C22 | semidirect |
| 30. #22575373 | C22 | semidirect |
| 31. #22575364 | C22 | semidirect |
| 32. C4×#14524130 | C22 | semidirect |
| 34. C4⋊Q8×C269 | C22 | semidirect |
| 36. #125×C269 | C22 | semidirect |
| 135. C269 | #3136 | semidirect |
| 137. #544 | D269 | semidirect |
| 153. C4⋊Q8 | C2×D269 | semidirect |
| 156. #125 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771174 | 2 |
| #31770971 | 2 |
| #31770967 | 2 |
| #31770962 | 2 |
| #31770953 | 2 |
| #31770609 | 2 |
| #31770604 | 2 |
| #31770599 | 2 |
| C2×#22575373 | 2 |
| #31770561 | 2 |
| #544×C269 | 2 |
| #3136 | 269 |