Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
382 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 382 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771333 | C2 | semidirect |
| 3. #31770970 | C2 | semidirect |
| 4. #31770952 | C2 | semidirect |
| 5. #31770906 | C2 | semidirect |
| 6. #31770886 | C2 | semidirect |
| 7. #31770806 | C2 | semidirect |
| 8. #31770806 | C2 | semidirect |
| 9. #31770707 | C2 | semidirect |
| 10. C4×#16864391 | C2 | semidirect |
| 11. #446×C269 | C2 | semidirect |
| 78. Dic538 | #41 | semidirect |
| 124. C269 | #3368 | semidirect |
| 134. #446 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771333 | 2 |
| #31771277 | 2 |
| #31770970 | 2 |
| #31770952 | 2 |
| #31770906 | 2 |
| #31770886 | 2 |
| #31770806 | 2 |
| #31770707 | 2 |
| C4×#16864391 | 2 |
| #446×C269 | 2 |
| #3368 | 269 |