Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
354 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 354 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. #31771008 | C2 | semidirect |
| 3. #31770943 | C2 | semidirect |
| 4. #31770918 | C2 | semidirect |
| 5. #31770900 | C2 | semidirect |
| 6. #31770892 | C2 | semidirect |
| 7. #31770853 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. #31770683 | C2 | semidirect |
| 10. #31770645 | C2 | semidirect |
| 11. #554×C269 | C2 | semidirect |
| 121. C269 | #3357 | semidirect |
| 124. #554 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771320 | 2 |
| #31771008 | 2 |
| #31770943 | 2 |
| #31770918 | 2 |
| #31770900 | 2 |
| #31770892 | 2 |
| #31770853 | 2 |
| C4×#16864389 | 2 |
| #31770683 | 2 |
| #31770645 | 2 |
| #554×C269 | 2 |
| #3357 | 269 |