Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
398 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 398 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31770902 | C2 | semidirect |
| 3. #31770902 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770882 | C2 | semidirect |
| 6. #31770645 | C2 | semidirect |
| 7. #31770641 | C2 | semidirect |
| 8. #31770632 | C2 | semidirect |
| 11. #544×C269 | C2 | semidirect |
| 21. #22575386 | C22 | semidirect |
| 22. #22575386 | C22 | semidirect |
| 23. #22575386 | C22 | semidirect |
| 24. #22575384 | C22 | semidirect |
| 25. #22575384 | C22 | semidirect |
| 26. #22575384 | C22 | semidirect |
| 27. C4⋊#14524130 | C22 | semidirect |
| 28. C4⋊#14524130 | C22 | semidirect |
| 34. C4⋊Q8×C269 | C22 | semidirect |
| 36. #125×C269 | C22 | semidirect |
| 44. C2×D1076 | Q8 | semidirect |
| 124. C269 | #3081 | semidirect |
| 126. #544 | D269 | semidirect |
| 141. C4⋊Q8 | C2×D269 | semidirect |
| 143. #125 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771079 | 2 |
| #31770902 | 2 |
| #31770892 | 2 |
| #31770882 | 2 |
| #31770645 | 2 |
| #31770641 | 2 |
| #31770632 | 2 |
| #31770609 | 2 |
| C2×#22575373 | 2 |
| #544×C269 | 2 |
| #3081 | 269 |