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 |
|---|---|---|
| 1. #31771233 | C2 | semidirect |
| 3. #31770906 | C2 | semidirect |
| 4. #31770906 | C2 | semidirect |
| 5. #31770896 | C2 | semidirect |
| 6. #31770886 | C2 | semidirect |
| 7. #31770647 | C2 | semidirect |
| 8. #31770643 | C2 | semidirect |
| 11. #424×C269 | C2 | semidirect |
| 13. #22575453 | C22 | semidirect |
| 15. #22575445 | C22 | semidirect |
| 26. #22575387 | C22 | semidirect |
| 27. #22575387 | C22 | semidirect |
| 28. #22575387 | C22 | semidirect |
| 29. #22575385 | C22 | semidirect |
| 30. #22575385 | C22 | semidirect |
| 31. #22575385 | C22 | semidirect |
| 39. C4⋊C8×C269 | C22 | semidirect |
| 40. C4⋊C8×C269 | C22 | semidirect |
| 45. C2×D1076 | Q8 | semidirect |
| 124. C269 | #3081 | semidirect |
| 134. #424 | D269 | semidirect |
| 160. C4⋊C8 | C2×D269 | semidirect |
| 161. 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 |
| #31771079 | 2 |
| #31770906 | 2 |
| #31770896 | 2 |
| #31770886 | 2 |
| #31770647 | 2 |
| #31770643 | 2 |
| #31770611 | 2 |
| C2×#22575375 | 2 |
| #424×C269 | 2 |
| #3081 | 269 |