Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
398 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 398 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. #31770908 | C2 | semidirect |
| 4. #31770904 | C2 | semidirect |
| 5. #31770894 | C2 | semidirect |
| 6. #31770884 | C2 | semidirect |
| 7. #31770648 | C2 | semidirect |
| 8. #31770631 | C2 | semidirect |
| 11. #427×C269 | C2 | semidirect |
| 15. #22575452 | C22 | semidirect |
| 17. #22575444 | C22 | semidirect |
| 26. #22575386 | C22 | semidirect |
| 27. #22575384 | C22 | semidirect |
| 28. #22575382 | C22 | semidirect |
| 29. #22575382 | C22 | semidirect |
| 37. #107×C269 | C22 | semidirect |
| 38. #107×C269 | C22 | semidirect |
| 39. #106×C269 | C22 | semidirect |
| 40. #106×C269 | C22 | semidirect |
| 45. C2×D1076 | Q8 | semidirect |
| 124. C269 | #3081 | semidirect |
| 133. #427 | D269 | semidirect |
| 155. #107 | C2×D269 | semidirect |
| 156. #107 | C2×D269 | semidirect |
| 158. #106 | C2×D269 | semidirect |
| 159. #106 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31771079 | 2 |
| #31770908 | 2 |
| #31770904 | 2 |
| #31770894 | 2 |
| #31770884 | 2 |
| #31770648 | 2 |
| #31770631 | 2 |
| #31770609 | 2 |
| C2×#22575375 | 2 |
| #427×C269 | 2 |
| #3081 | 269 |