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 |
|---|---|---|
| 1. #31771233 | C2 | semidirect |
| 3. #31770970 | C2 | semidirect |
| 4. #31770965 | C2 | semidirect |
| 5. #31770960 | C2 | semidirect |
| 6. #31770952 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770607 | C2 | semidirect |
| 9. #31770602 | C2 | semidirect |
| 10. C2×#22575375 | C2 | semidirect |
| 11. #405×C269 | C2 | semidirect |
| 14. #22575453 | C22 | semidirect |
| 17. #22575445 | C22 | semidirect |
| 26. #22575378 | C22 | semidirect |
| 27. #22575378 | C22 | semidirect |
| 28. #22575378 | C22 | semidirect |
| 33. #22575375 | C22 | semidirect |
| 34. #22575375 | C22 | semidirect |
| 35. #22575375 | C22 | semidirect |
| 39. #97×C269 | C22 | semidirect |
| 40. C4×C8×C269 | C22 | semidirect |
| 135. C269 | #3136 | semidirect |
| 147. #405 | D269 | semidirect |
| 175. #97 | C2×D269 | semidirect |
| 176. C4×C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31771174 | 2 |
| #31770970 | 2 |
| #31770965 | 2 |
| #31770960 | 2 |
| #31770952 | 2 |
| #31770611 | 2 |
| #31770607 | 2 |
| #31770602 | 2 |
| C2×#22575375 | 2 |
| #405×C269 | 2 |
| #3136 | 269 |