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. #31770958 | C2 | semidirect |
| 5. #31770907 | C2 | semidirect |
| 6. #31770891 | C2 | semidirect |
| 7. #31770825 | C2 | semidirect |
| 8. #31770729 | C2 | semidirect |
| 9. C4×#16864392 | C2 | semidirect |
| 10. SD16×Dic269 | C2 | semidirect |
| 117. C269 | #3365 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771341 | 2 |
| #31771334 | 2 |
| #31770958 | 2 |
| #31770951 | 2 |
| #31770907 | 2 |
| #31770891 | 2 |
| #31770825 | 2 |
| #31770729 | 2 |
| C4×#16864392 | 2 |
| SD16×Dic269 | 2 |
| #460×C269 | 2 |
| #3365 | 269 |