Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
264 conjugacy classes of subgroups; only the 69 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 69 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. #31770655 | C2 | semidirect |
| 3. #31770469 | C2 | semidirect |
| 4. #31770340 | C2 | semidirect |
| 5. #31770339 | C2 | semidirect |
| 6. #31770338 | C2 | semidirect |
| 7. #327×C269 | C2 | semidirect |
| 9. #22575452 | C4 | semidirect |
| 10. #22575449 | C4 | semidirect |
| 14. D4×Dic269 | C4 | semidirect |
| 15. #22575415 | C4 | semidirect |
| 119. C269 | #1517 | semidirect |
| 127. #327 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771150 | 2 |
| #31770655 | 2 |
| #31770469 | 2 |
| #31770340 | 2 |
| #31770339 | 2 |
| #31770338 | 2 |
| #327×C269 | 2 |
| #1517 | 269 |