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×#22575481 | C2 | semidirect |
| 2. C2×#22575473 | C2 | semidirect |
| 3. #31771169 | C2 | semidirect |
| 4. #31771086 | C2 | semidirect |
| 5. #31770830 | C2 | semidirect |
| 6. #31770823 | C2 | semidirect |
| 7. #31770804 | C2 | semidirect |
| 8. #31770799 | C2 | semidirect |
| 9. #31770633 | C2 | semidirect |
| 10. C2×#22575373 | C2 | semidirect |
| 11. #417×C269 | C2 | semidirect |
| 16. C2×#16864392 | C22 | semidirect |
| 18. C2×#16864390 | C22 | semidirect |
| 19. C2×#16864389 | C22 | semidirect |
| 21. C2×#16864387 | C22 | semidirect |
| 28. #22575418 | C22 | semidirect |
| 29. #22575415 | C22 | semidirect |
| 34. #22575382 | C22 | semidirect |
| 35. #22575382 | C22 | semidirect |
| 41. #103×C269 | C22 | semidirect |
| 42. #102×C269 | C22 | semidirect |
| 45. #16864402 | D4 | semidirect |
| 154. C269 | #3045 | semidirect |
| 165. #417 | D269 | semidirect |
| 194. #103 | C2×D269 | semidirect |
| 197. #102 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575481 | 2 |
| C2×#22575473 | 2 |
| #31771169 | 2 |
| #31771086 | 2 |
| #31770830 | 2 |
| #31770823 | 2 |
| #31770804 | 2 |
| #31770799 | 2 |
| #31770633 | 2 |
| C2×#22575373 | 2 |
| #417×C269 | 2 |
| #3045 | 269 |