Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
466 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31771405 | C2 | semidirect |
| 2. C2×#22575479 | C2 | semidirect |
| 3. C2×#22575479 | C2 | semidirect |
| 4. #31771371 | C2 | semidirect |
| 5. #31770874 | C2 | semidirect |
| 6. #31770867 | C2 | semidirect |
| 7. #31770653 | C2 | semidirect |
| 8. #31770587 | C2 | semidirect |
| 9. C2×#100×C269 | C2 | semidirect |
| 13. #22575486 | C22 | semidirect |
| 15. #22575481 | C22 | semidirect |
| 22. C2×#16864390 | C22 | semidirect |
| 24. C2×#16864387 | C22 | semidirect |
| 25. #22575461 | C22 | semidirect |
| 30. #22575388 | C22 | semidirect |
| 31. #22575371 | C22 | semidirect |
| 32. #22575369 | C22 | semidirect |
| 36. #100×C269 | C22 | semidirect |
| 147. C269 | #3068 | semidirect |
| 157. C2×#100 | D269 | semidirect |
| 184. #100 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771405 | 2 |
| C2×#22575479 | 2 |
| #31771371 | 2 |
| #31770874 | 2 |
| #31770867 | 2 |
| #31770653 | 2 |
| #31770587 | 2 |
| C2×#100×C269 | 2 |
| #3068 | 269 |