Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
404 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 404 conjugacy classes of subgroups — too many to draw. Only its 125 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. #31771236 | C2 | semidirect |
| 3. #31770968 | C2 | semidirect |
| 4. #31770966 | C2 | semidirect |
| 5. #31770961 | C2 | semidirect |
| 6. #31770950 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770601 | C2 | semidirect |
| 9. C2×#22575373 | C2 | semidirect |
| 10. #31770563 | C2 | semidirect |
| 11. #417×C269 | C2 | semidirect |
| 15. #22575452 | C22 | semidirect |
| 18. #22575444 | C22 | semidirect |
| 26. #22575377 | C22 | semidirect |
| 27. #22575377 | C22 | semidirect |
| 30. #22575374 | C22 | semidirect |
| 31. #22575374 | C22 | semidirect |
| 34. #22575363 | C22 | semidirect |
| 35. C8×Dic269 | C22 | semidirect |
| 39. #103×C269 | C22 | semidirect |
| 40. #102×C269 | C22 | semidirect |
| 135. C269 | #3136 | semidirect |
| 144. #417 | D269 | semidirect |
| 167. #103 | C2×D269 | semidirect |
| 174. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771236 | 2 |
| #31771169 | 2 |
| #31770968 | 2 |
| #31770966 | 2 |
| #31770961 | 2 |
| #31770950 | 2 |
| #31770611 | 2 |
| #31770601 | 2 |
| C2×#22575373 | 2 |
| #31770563 | 2 |
| #417×C269 | 2 |
| #3136 | 269 |