Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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. #31770945 | C2 | semidirect |
| 4. #31770890 | C2 | semidirect |
| 5. #31770886 | C2 | semidirect |
| 6. #31770807 | C2 | semidirect |
| 8. Q16×Dic269 | C2 | semidirect |
| 9. #31770690 | C2 | semidirect |
| 10. #31770657 | C2 | semidirect |
| 11. #462×C269 | C2 | semidirect |
| 136. C269 | #3107 | semidirect |
| 143. #462 | 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 |
| #31770945 | 2 |
| #31770890 | 2 |
| #31770886 | 2 |
| #31770807 | 2 |
| #31770766 | 2 |
| Q16×Dic269 | 2 |
| #31770690 | 2 |
| #31770657 | 2 |
| #462×C269 | 2 |
| #3107 | 269 |