Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 119 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 119 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 |
|---|---|---|
| 1. #31771160 | C2 | semidirect |
| 3. #31770948 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770815 | C2 | semidirect |
| 6. #31770811 | C2 | semidirect |
| 8. #31770709 | C2 | semidirect |
| 9. #31770704 | C2 | semidirect |
| 10. #31770661 | C2 | semidirect |
| 11. #477×C269 | C2 | semidirect |
| 136. C269 | #3116 | semidirect |
| 141. #477 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771160 | 2 |
| C4×#16864403 | 2 |
| #31770948 | 2 |
| #31770892 | 2 |
| #31770815 | 2 |
| #31770811 | 2 |
| #31770770 | 2 |
| #31770709 | 2 |
| #31770704 | 2 |
| #31770661 | 2 |
| #477×C269 | 2 |
| #3116 | 269 |