Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
348 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 2. #31771330 | C2 | semidirect |
| 3. #31770961 | C2 | semidirect |
| 5. #31770904 | C2 | semidirect |
| 6. #31770830 | C2 | semidirect |
| 8. #31770729 | C2 | semidirect |
| 9. C4×#16864392 | C2 | semidirect |
| 10. #31770692 | C2 | semidirect |
| 11. #475×C269 | C2 | semidirect |
| 117. C269 | #3365 | semidirect |
| 124. #475 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771340 | 2 |
| #31771330 | 2 |
| #31770961 | 2 |
| #31770953 | 2 |
| #31770904 | 2 |
| #31770830 | 2 |
| #31770806 | 2 |
| #31770729 | 2 |
| C4×#16864392 | 2 |
| #31770692 | 2 |
| #475×C269 | 2 |
| #3365 | 269 |