Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
504 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22575481 | C2 | semidirect |
| 2. #31771183 | C2 | semidirect |
| 3. #31771169 | C2 | semidirect |
| 4. #31770858 | C2 | semidirect |
| 5. #31770851 | C2 | semidirect |
| 6. #31770841 | C2 | semidirect |
| 7. #31770834 | C2 | semidirect |
| 8. #31770647 | C2 | semidirect |
| 9. #31770602 | C2 | semidirect |
| 10. C2×#22575375 | C2 | semidirect |
| 11. C2×#131×C269 | C2 | semidirect |
| 19. #22575432 | C22 | semidirect |
| 23. #22575427 | C22 | semidirect |
| 29. #22575387 | C22 | semidirect |
| 30. #22575385 | C22 | semidirect |
| 31. #22575378 | C22 | semidirect |
| 32. #22575378 | C22 | semidirect |
| 35. #22575375 | C22 | semidirect |
| 36. #22575375 | C22 | semidirect |
| 40. C2×M16×C269 | C22 | semidirect |
| 42. C22×C8×C269 | C22 | semidirect |
| 79. M16×C269 | D4 | semidirect |
| 151. C269 | #3062 | semidirect |
| 154. C2×#131 | D269 | semidirect |
| 172. C2×M16 | C2×D269 | semidirect |
| 174. C22×C8 | C2×D269 | semidirect |
| 220. M16 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| #31771183 | 2 |
| #31771169 | 2 |
| #31770858 | 2 |
| #31770851 | 2 |
| #31770841 | 2 |
| #31770834 | 2 |
| #31770647 | 2 |
| #31770602 | 2 |
| C2×#22575375 | 2 |
| C2×#131×C269 | 2 |
| #3062 | 269 |