Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. C2×C4×Dic538 | C2 | semidirect |
| 3. #31770941 | C2 | semidirect |
| 5. #31770913 | C2 | semidirect |
| 6. #31770828 | C2 | semidirect |
| 7. #31770763 | C2 | semidirect |
| 9. #31770713 | C2 | semidirect |
| 10. #31770707 | C2 | semidirect |
| 11. #432×C269 | C2 | semidirect |
| 131. C269 | #3117 | semidirect |
| 143. #432 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771139 | 2 |
| C2×C4×Dic538 | 2 |
| #31770941 | 2 |
| #31770924 | 2 |
| #31770913 | 2 |
| #31770828 | 2 |
| #31770763 | 2 |
| #31770746 | 2 |
| #31770713 | 2 |
| #31770707 | 2 |
| #432×C269 | 2 |
| #3117 | 269 |