Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
310 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 89 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 |
|---|---|---|
| 3. #31770614 | C2 | semidirect |
| 5. #31770375 | C2 | semidirect |
| 6. #31770361 | C2 | semidirect |
| 7. #519×C269 | C2 | semidirect |
| 11. C2×#16864392 | C4 | semidirect |
| 12. C2×#16864389 | C4 | semidirect |
| 109. C269 | #1905 | semidirect |
| 112. #519 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| #31770623 | 2 |
| #31770614 | 2 |
| #31770578 | 2 |
| #31770375 | 2 |
| #31770361 | 2 |
| #519×C269 | 2 |
| #1905 | 269 |