Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
494 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 494 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. C22×#16864391 | C2 | semidirect |
| 3. #31771181 | C2 | semidirect |
| 4. #31771079 | C2 | semidirect |
| 5. #31770821 | C2 | semidirect |
| 6. #31770811 | C2 | semidirect |
| 7. #31770615 | C2 | semidirect |
| 8. #31770602 | C2 | semidirect |
| 9. #424×C269 | C2 | semidirect |
| 18. #22575453 | C22 | semidirect |
| 19. #22575441 | C22 | semidirect |
| 26. #22575378 | C22 | semidirect |
| 27. #22575378 | C22 | semidirect |
| 28. #22575375 | C22 | semidirect |
| 32. C4⋊C8×C269 | C22 | semidirect |
| 116. C269 | #3042 | semidirect |
| 124. #424 | D269 | semidirect |
| 146. C4⋊C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| C22×#16864391 | 2 |
| #31771181 | 2 |
| #31771079 | 2 |
| #31770821 | 2 |
| #31770811 | 2 |
| #31770615 | 2 |
| #31770602 | 2 |
| #424×C269 | 2 |
| #3042 | 269 |