Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
338 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 3. #31770957 | C2 | semidirect |
| 5. #31770887 | C2 | semidirect |
| 7. #31770815 | C2 | semidirect |
| 8. #31770736 | C2 | semidirect |
| 9. #31770710 | C2 | semidirect |
| 11. Q82×C269 | C2 | semidirect |
| 116. C269 | #3369 | semidirect |
| 118. Q82 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| #31770967 | 2 |
| #31770957 | 2 |
| #31770892 | 2 |
| #31770887 | 2 |
| #31770827 | 2 |
| #31770815 | 2 |
| #31770736 | 2 |
| #31770710 | 2 |
| C4×#16864389 | 2 |
| Q82×C269 | 2 |
| #3369 | 269 |