Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
420 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 137 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 |
|---|---|---|
| 2. C2×#22575412 | C2 | semidirect |
| 3. #31770947 | C2 | semidirect |
| 4. #31770941 | C2 | semidirect |
| 5. #31770936 | C2 | semidirect |
| 6. #31770930 | C2 | semidirect |
| 7. #31770924 | C2 | semidirect |
| 8. #31770919 | C2 | semidirect |
| 9. #31770643 | C2 | semidirect |
| 10. #31770602 | C2 | semidirect |
| 11. C2×C22⋊C8×C269 | C2 | semidirect |
| 30. #22575387 | C22 | semidirect |
| 31. #22575387 | C22 | semidirect |
| 32. #22575385 | C22 | semidirect |
| 33. #22575385 | C22 | semidirect |
| 34. #22575378 | C22 | semidirect |
| 35. #22575378 | C22 | semidirect |
| 36. #22575375 | C22 | semidirect |
| 37. #22575375 | C22 | semidirect |
| 143. C269 | #3091 | semidirect |
| 155. C2×C22⋊C8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771116 | 2 |
| C2×#22575412 | 2 |
| #31770947 | 2 |
| #31770941 | 2 |
| #31770936 | 2 |
| #31770930 | 2 |
| #31770924 | 2 |
| #31770919 | 2 |
| #31770643 | 2 |
| #31770602 | 2 |
| C2×C22⋊C8×C269 | 2 |
| #3091 | 269 |