Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
784 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 784 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575499 | C2 | semidirect |
| 2. C2×#22575478 | C2 | semidirect |
| 3. C22×D2152 | C2 | semidirect |
| 4. #31771174 | C2 | semidirect |
| 5. #31770753 | C2 | semidirect |
| 6. #31770740 | C2 | semidirect |
| 7. #31770609 | C2 | semidirect |
| 8. #31770571 | C2 | semidirect |
| 9. #416×C269 | C2 | semidirect |
| 12. C2×#16864403 | C22 | semidirect |
| 17. C22×D1076 | C22 | semidirect |
| 19. C2×D4×D269 | C22 | semidirect |
| 21. C2×#16864389 | C22 | semidirect |
| 23. C2×D2152 | C22 | semidirect |
| 24. C2×#16864387 | C22 | semidirect |
| 25. C2×#16864386 | C22 | semidirect |
| 28. #22575428 | C22 | semidirect |
| 30. #22575373 | C22 | semidirect |
| 31. #22575365 | C22 | semidirect |
| 33. C22×C8×C269 | C22 | semidirect |
| 34. #117×C269 | C22 | semidirect |
| 35. #103×C269 | C22 | semidirect |
| 36. #102×C269 | C22 | semidirect |
| 55. C2×D1076 | D4 | semidirect |
| 72. #41×C269 | D4 | semidirect |
| 151. C269 | #3008 | semidirect |
| 160. #416 | D269 | semidirect |
| 179. C22×C8 | C2×D269 | semidirect |
| 184. #117 | C2×D269 | semidirect |
| 185. #103 | C2×D269 | semidirect |
| 187. #102 | C2×D269 | semidirect |
| 198. #41 | D1076 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575499 | 2 |
| C2×#22575478 | 2 |
| C22×D2152 | 2 |
| #31771174 | 2 |
| #31770753 | 2 |
| #31770740 | 2 |
| #31770609 | 2 |
| #31770571 | 2 |
| #416×C269 | 2 |
| #3008 | 269 |