Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
404 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 404 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. #31771233 | C2 | semidirect |
| 2. #31770969 | C2 | semidirect |
| 3. #31770964 | C2 | semidirect |
| 4. #31770959 | C2 | semidirect |
| 5. #31770951 | C2 | semidirect |
| 6. #31770610 | C2 | semidirect |
| 7. #31770606 | C2 | semidirect |
| 8. #31770601 | C2 | semidirect |
| 9. C2×#22575374 | C2 | semidirect |
| 10. #31770561 | C2 | semidirect |
| 14. #22575453 | C22 | semidirect |
| 16. #22575445 | C22 | semidirect |
| 21. #22575377 | C22 | semidirect |
| 22. #22575377 | C22 | semidirect |
| 23. #22575377 | C22 | semidirect |
| 28. #22575374 | C22 | semidirect |
| 29. #22575374 | C22 | semidirect |
| 30. #22575374 | C22 | semidirect |
| 31. #22575364 | C22 | semidirect |
| 32. C4×#14524130 | C22 | semidirect |
| 135. C269 | #3136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31770969 | 2 |
| #31770964 | 2 |
| #31770959 | 2 |
| #31770951 | 2 |
| #31770610 | 2 |
| #31770606 | 2 |
| #31770601 | 2 |
| C2×#22575374 | 2 |
| #31770561 | 2 |
| #535×C269 | 2 |
| #3136 | 269 |