Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 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×#22575444 | C2 | semidirect |
| 3. #31770972 | C2 | semidirect |
| 4. #31770968 | C2 | semidirect |
| 5. #31770961 | C2 | semidirect |
| 6. #31770958 | C2 | semidirect |
| 7. #31770607 | C2 | semidirect |
| 8. #31770606 | C2 | semidirect |
| 9. #31770604 | C2 | semidirect |
| 10. M16×Dic269 | C2 | semidirect |
| 11. #417×C269 | C2 | semidirect |
| 146. C269 | #3142 | semidirect |
| 157. #417 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771151 | 2 |
| C2×#22575444 | 2 |
| #31770972 | 2 |
| #31770968 | 2 |
| #31770961 | 2 |
| #31770958 | 2 |
| #31770607 | 2 |
| #31770606 | 2 |
| #31770604 | 2 |
| M16×Dic269 | 2 |
| #417×C269 | 2 |
| #3142 | 269 |