Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
526 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 526 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. C22×#16864387 | C2 | semidirect |
| 2. #31771169 | C2 | semidirect |
| 3. #31771080 | C2 | semidirect |
| 4. #31770822 | C2 | semidirect |
| 5. #31770798 | C2 | semidirect |
| 6. #31770633 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770601 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C269 | C2 | semidirect |
| 14. #22575449 | C22 | semidirect |
| 15. #22575442 | C22 | semidirect |
| 19. D4×Dic269 | C22 | semidirect |
| 23. #22575382 | C22 | semidirect |
| 24. #22575377 | C22 | semidirect |
| 25. #22575375 | C22 | semidirect |
| 26. #22575374 | C22 | semidirect |
| 30. C2×SD16×C269 | C22 | semidirect |
| 31. C2×D8×C269 | C22 | semidirect |
| 58. C2×D4×C269 | D4 | semidirect |
| 121. C269 | #3041 | semidirect |
| 123. C2×AGL(1,ℤ/8) | D269 | semidirect |
| 136. C2×SD16 | C2×D269 | semidirect |
| 139. C2×D8 | C2×D269 | semidirect |
| 168. C2×D4 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864387 | 2 |
| #31771169 | 2 |
| #31771080 | 2 |
| #31770822 | 2 |
| #31770798 | 2 |
| #31770633 | 2 |
| #31770611 | 2 |
| #31770601 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #3041 | 269 |