Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771329 | C2 | semidirect |
| 3. #31770957 | C2 | semidirect |
| 4. #31770948 | C2 | semidirect |
| 5. #31770847 | C2 | semidirect |
| 6. #31770816 | C2 | semidirect |
| 7. #31770768 | C2 | semidirect |
| 8. C4×#16864390 | C2 | semidirect |
| 9. #31770670 | C2 | semidirect |
| 10. #31770598 | C2 | semidirect |
| 11. #474×C269 | C2 | semidirect |
| 125. C269 | #3302 | semidirect |
| 131. #474 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771329 | 2 |
| #31771259 | 2 |
| #31770957 | 2 |
| #31770948 | 2 |
| #31770847 | 2 |
| #31770816 | 2 |
| #31770768 | 2 |
| C4×#16864390 | 2 |
| #31770670 | 2 |
| #31770598 | 2 |
| #474×C269 | 2 |
| #3302 | 269 |