Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 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. C2×#22575473 | C2 | semidirect |
| 2. #31771172 | C2 | semidirect |
| 3. #31771088 | C2 | semidirect |
| 4. #31770825 | C2 | semidirect |
| 5. #31770818 | C2 | semidirect |
| 6. #31770803 | C2 | semidirect |
| 7. #31770798 | C2 | semidirect |
| 8. #31770633 | C2 | semidirect |
| 9. #31770607 | C2 | semidirect |
| 10. C2×#22575374 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C269 | C2 | semidirect |
| 14. C2×#16864392 | C22 | semidirect |
| 15. C2×#16864390 | C22 | semidirect |
| 16. C2×#16864389 | C22 | semidirect |
| 17. C2×#16864387 | C22 | semidirect |
| 24. Q8×Dic269 | C22 | semidirect |
| 26. D4×Dic269 | C22 | semidirect |
| 31. #22575382 | C22 | semidirect |
| 32. #22575382 | C22 | semidirect |
| 33. #22575378 | C22 | semidirect |
| 34. #22575375 | C22 | semidirect |
| 73. #41×C269 | D4 | semidirect |
| 154. C269 | #3045 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D269 | semidirect |
| 202. #41 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575473 | 2 |
| #31771172 | 2 |
| #31771088 | 2 |
| #31770825 | 2 |
| #31770818 | 2 |
| #31770803 | 2 |
| #31770798 | 2 |
| #31770633 | 2 |
| #31770607 | 2 |
| C2×#22575374 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #3045 | 269 |