Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
348 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 123 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. #31771333 | C2 | semidirect |
| 3. #31770960 | C2 | semidirect |
| 5. #31770906 | C2 | semidirect |
| 6. #31770891 | C2 | semidirect |
| 7. #31770828 | C2 | semidirect |
| 9. C4×Dic1076 | C2 | semidirect |
| 10. C4×#16864391 | C2 | semidirect |
| 11. C8×Q8×C269 | C2 | semidirect |
| 117. C269 | #3365 | semidirect |
| 127. C8×Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771340 | 2 |
| #31771333 | 2 |
| #31770960 | 2 |
| #31770952 | 2 |
| #31770906 | 2 |
| #31770891 | 2 |
| #31770828 | 2 |
| #31770806 | 2 |
| C4×Dic1076 | 2 |
| C4×#16864391 | 2 |
| C8×Q8×C269 | 2 |
| #3365 | 269 |