Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
526 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 526 conjugacy classes of subgroups — too many to draw. Only its 133 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×#22575478 | C2 | semidirect |
| 2. C22×D2152 | C2 | semidirect |
| 3. #31771169 | C2 | semidirect |
| 4. #31771079 | C2 | semidirect |
| 5. #31770823 | C2 | semidirect |
| 6. #31770799 | C2 | semidirect |
| 7. #31770631 | C2 | semidirect |
| 8. #31770609 | C2 | semidirect |
| 9. #416×C269 | C2 | semidirect |
| 13. C2×#16864389 | C22 | semidirect |
| 16. C2×#16864387 | C22 | semidirect |
| 18. #22575449 | C22 | semidirect |
| 19. #22575442 | C22 | semidirect |
| 23. #22575415 | C22 | semidirect |
| 26. #22575382 | C22 | semidirect |
| 27. #22575373 | C22 | semidirect |
| 31. #103×C269 | C22 | semidirect |
| 32. #102×C269 | C22 | semidirect |
| 40. C2×D1076 | D4 | semidirect |
| 121. C269 | #3041 | semidirect |
| 131. #416 | D269 | semidirect |
| 152. #103 | C2×D269 | semidirect |
| 154. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575478 | 2 |
| C22×D2152 | 2 |
| #31771169 | 2 |
| #31771079 | 2 |
| #31770823 | 2 |
| #31770799 | 2 |
| #31770631 | 2 |
| #31770609 | 2 |
| #416×C269 | 2 |
| #3041 | 269 |