Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
382 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 382 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 |
|---|---|---|
| 1. #31771330 | C2 | semidirect |
| 3. #31770968 | C2 | semidirect |
| 4. #31770953 | C2 | semidirect |
| 5. #31770908 | C2 | semidirect |
| 6. #31770806 | C2 | semidirect |
| 7. #31770804 | C2 | semidirect |
| 8. #31770732 | C2 | semidirect |
| 9. #31770704 | C2 | semidirect |
| 10. C4×#16864390 | C2 | semidirect |
| 11. #474×C269 | C2 | semidirect |
| 77. Dic538 | #41 | semidirect |
| 124. C269 | #3368 | semidirect |
| 131. #474 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771330 | 2 |
| #31771276 | 2 |
| #31770968 | 2 |
| #31770953 | 2 |
| #31770908 | 2 |
| #31770806 | 2 |
| #31770804 | 2 |
| #31770732 | 2 |
| #31770704 | 2 |
| C4×#16864390 | 2 |
| #474×C269 | 2 |
| #3368 | 269 |