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. C22×#16864387 | C2 | semidirect |
| 3. #31771172 | C2 | semidirect |
| 4. #31770749 | C2 | semidirect |
| 5. #31770737 | C2 | semidirect |
| 6. #31770611 | C2 | semidirect |
| 7. #31770601 | C2 | semidirect |
| 8. #31770573 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C269 | C2 | semidirect |
| 12. C2×#16864403 | C22 | semidirect |
| 18. C2×D4×D269 | C22 | semidirect |
| 20. C2×#16864387 | C22 | semidirect |
| 21. C22×#14524130 | C22 | semidirect |
| 24. #22575424 | C22 | semidirect |
| 26. #22575412 | C22 | semidirect |
| 27. #22575377 | C22 | semidirect |
| 28. #22575375 | C22 | semidirect |
| 29. #22575374 | C22 | semidirect |
| 30. #22575365 | C22 | semidirect |
| 32. C22×D4×C269 | C22 | semidirect |
| 34. C2×SD16×C269 | C22 | semidirect |
| 35. C2×D8×C269 | C22 | semidirect |
| 36. C2×M16×C269 | C22 | semidirect |
| 50. C2×D1076 | D4 | semidirect |
| 69. #41×C269 | D4 | semidirect |
| 151. C269 | #3008 | semidirect |
| 154. C2×AGL(1,ℤ/8) | D269 | semidirect |
| 172. C22×D4 | C2×D269 | semidirect |
| 174. C2×SD16 | C2×D269 | semidirect |
| 177. C2×D8 | C2×D269 | semidirect |
| 178. C2×M16 | C2×D269 | semidirect |
| 198. #41 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575499 | 2 |
| C22×#16864387 | 2 |
| #31771172 | 2 |
| #31770749 | 2 |
| #31770737 | 2 |
| #31770611 | 2 |
| #31770601 | 2 |
| #31770573 | 2 |
| C2×AGL(1,ℤ/8)×C269 | 2 |
| #3008 | 269 |