Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
504 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575460 | C2 | semidirect |
| 3. #31771169 | C2 | semidirect |
| 4. #31770856 | C2 | semidirect |
| 5. #31770853 | C2 | semidirect |
| 6. #31770839 | C2 | semidirect |
| 7. #31770836 | C2 | semidirect |
| 8. #31770645 | C2 | semidirect |
| 9. #31770601 | C2 | semidirect |
| 10. C2×#22575373 | C2 | semidirect |
| 11. #537×C269 | C2 | semidirect |
| 18. C2×#16864386 | C22 | semidirect |
| 20. C22×#14524130 | C22 | semidirect |
| 27. #22575386 | C22 | semidirect |
| 28. #22575384 | C22 | semidirect |
| 29. #22575377 | C22 | semidirect |
| 30. #22575377 | C22 | semidirect |
| 31. #22575374 | C22 | semidirect |
| 32. #22575374 | C22 | semidirect |
| 38. C22⋊Q8×C269 | C22 | semidirect |
| 41. #121×C269 | C22 | semidirect |
| 53. #16864386 | D4 | semidirect |
| 151. C269 | #3062 | semidirect |
| 155. #537 | D269 | semidirect |
| 178. C22⋊Q8 | C2×D269 | semidirect |
| 183. #121 | 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×#22575460 | 2 |
| #31771169 | 2 |
| #31770856 | 2 |
| #31770853 | 2 |
| #31770839 | 2 |
| #31770836 | 2 |
| #31770645 | 2 |
| #31770601 | 2 |
| C2×#22575373 | 2 |
| #537×C269 | 2 |
| #3062 | 269 |