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×#22575479 | C2 | semidirect |
| 2. C2×#22575473 | C2 | semidirect |
| 3. #31771085 | C2 | semidirect |
| 4. #31770824 | C2 | semidirect |
| 5. #31770817 | C2 | semidirect |
| 6. #31770802 | C2 | semidirect |
| 7. #31770797 | C2 | semidirect |
| 8. #31770632 | C2 | semidirect |
| 9. #31770606 | C2 | semidirect |
| 10. C2×#22575374 | C2 | semidirect |
| 11. #535×C269 | C2 | semidirect |
| 15. C2×#16864392 | C22 | semidirect |
| 17. C2×#16864390 | C22 | semidirect |
| 18. C2×#16864389 | C22 | semidirect |
| 20. C2×#16864387 | C22 | semidirect |
| 23. C4×Dic538 | C22 | semidirect |
| 24. C4×D1076 | C22 | semidirect |
| 29. C4⋊#14524130 | C22 | semidirect |
| 30. C4⋊#14524130 | C22 | semidirect |
| 31. #22575377 | C22 | semidirect |
| 34. #22575374 | C22 | semidirect |
| 44. #16864402 | D4 | semidirect |
| 154. C269 | #3045 | semidirect |
| 158. #535 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575479 | 2 |
| C2×#22575473 | 2 |
| #31771085 | 2 |
| #31770824 | 2 |
| #31770817 | 2 |
| #31770802 | 2 |
| #31770797 | 2 |
| #31770632 | 2 |
| #31770606 | 2 |
| C2×#22575374 | 2 |
| #535×C269 | 2 |
| #3045 | 269 |