Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
390 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31770936 | C2 | semidirect |
| 5. #31770913 | C2 | semidirect |
| 6. #31770828 | C2 | semidirect |
| 7. #31770763 | C2 | semidirect |
| 9. C4×Dic1076 | C2 | semidirect |
| 10. C4×#16864391 | C2 | semidirect |
| 11. #431×C269 | C2 | semidirect |
| 131. C269 | #3108 | semidirect |
| 143. #431 | 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 |
| #31770936 | 2 |
| #31770919 | 2 |
| #31770913 | 2 |
| #31770828 | 2 |
| #31770763 | 2 |
| #31770746 | 2 |
| C4×Dic1076 | 2 |
| C4×#16864391 | 2 |
| #431×C269 | 2 |
| #3108 | 269 |