Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
348 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 348 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 |
|---|---|---|
| 2. #31771334 | C2 | semidirect |
| 3. #31770961 | C2 | semidirect |
| 5. #31770908 | C2 | semidirect |
| 6. #31770890 | C2 | semidirect |
| 7. #31770829 | C2 | semidirect |
| 9. C8×Dic538 | C2 | semidirect |
| 10. #31770690 | C2 | semidirect |
| 11. C4×Q16×C269 | C2 | semidirect |
| 117. C269 | #3365 | semidirect |
| 128. C4×Q16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771340 | 2 |
| #31771334 | 2 |
| #31770961 | 2 |
| #31770952 | 2 |
| #31770908 | 2 |
| #31770890 | 2 |
| #31770829 | 2 |
| #31770805 | 2 |
| C8×Dic538 | 2 |
| #31770690 | 2 |
| C4×Q16×C269 | 2 |
| #3365 | 269 |