Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
504 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 504 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. C2×#22575459 | C2 | semidirect |
| 3. #31771183 | C2 | semidirect |
| 4. #31771174 | C2 | semidirect |
| 5. #31770857 | C2 | semidirect |
| 6. #31770854 | C2 | semidirect |
| 7. #31770840 | C2 | semidirect |
| 8. #31770837 | C2 | semidirect |
| 9. #31770648 | C2 | semidirect |
| 10. C2×#22575375 | C2 | semidirect |
| 11. #416×C269 | C2 | semidirect |
| 19. C2×#16864385 | C22 | semidirect |
| 20. C2×C8×D269 | C22 | semidirect |
| 24. #22575429 | C22 | semidirect |
| 29. #22575424 | C22 | semidirect |
| 32. #22575386 | C22 | semidirect |
| 33. #22575384 | C22 | semidirect |
| 39. #103×C269 | C22 | semidirect |
| 40. #103×C269 | C22 | semidirect |
| 41. #102×C269 | C22 | semidirect |
| 42. #102×C269 | C22 | semidirect |
| 60. #16864386 | D4 | semidirect |
| 151. C269 | #3062 | semidirect |
| 162. #416 | D269 | semidirect |
| 189. #103 | C2×D269 | semidirect |
| 190. #103 | C2×D269 | semidirect |
| 193. #102 | C2×D269 | semidirect |
| 194. #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 |
| C2×#22575459 | 2 |
| #31771183 | 2 |
| #31771174 | 2 |
| #31770857 | 2 |
| #31770854 | 2 |
| #31770840 | 2 |
| #31770837 | 2 |
| #31770648 | 2 |
| C2×#22575375 | 2 |
| #416×C269 | 2 |
| #3062 | 269 |