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. C2×#22575481 | C2 | semidirect |
| 2. C22×D2152 | C2 | semidirect |
| 3. #31771174 | C2 | semidirect |
| 4. #31771079 | C2 | semidirect |
| 5. #31770821 | C2 | semidirect |
| 6. #31770801 | C2 | semidirect |
| 7. #31770611 | C2 | semidirect |
| 8. #31770602 | C2 | semidirect |
| 9. #424×C269 | C2 | semidirect |
| 14. C2×#16864391 | C22 | semidirect |
| 17. C2×D2152 | C22 | semidirect |
| 18. #22575450 | C22 | semidirect |
| 19. #22575441 | C22 | semidirect |
| 22. C4×D1076 | C22 | semidirect |
| 26. #22575378 | C22 | semidirect |
| 27. #22575375 | C22 | semidirect |
| 28. #22575375 | C22 | semidirect |
| 32. C4⋊C8×C269 | C22 | semidirect |
| 44. C2×D1076 | D4 | semidirect |
| 121. C269 | #3041 | semidirect |
| 129. #424 | D269 | semidirect |
| 151. 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×D2152 | 2 |
| #31771174 | 2 |
| #31771079 | 2 |
| #31770821 | 2 |
| #31770801 | 2 |
| #31770611 | 2 |
| #31770602 | 2 |
| #424×C269 | 2 |
| #3041 | 269 |