Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 113 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. #31771156 | C2 | semidirect |
| 2. #31771137 | C2 | semidirect |
| 3. #31770908 | C2 | semidirect |
| 4. #31770887 | C2 | semidirect |
| 5. #31770857 | C2 | semidirect |
| 6. #31770852 | C2 | semidirect |
| 7. #31770819 | C2 | semidirect |
| 8. #31770806 | C2 | semidirect |
| 9. #31770800 | C2 | semidirect |
| 10. #31770627 | C2 | semidirect |
| 11. #474×C269 | C2 | semidirect |
| 141. C269 | #3251 | semidirect |
| 147. #474 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771156 | 2 |
| #31771137 | 2 |
| #31770908 | 2 |
| #31770887 | 2 |
| #31770857 | 2 |
| #31770852 | 2 |
| #31770819 | 2 |
| #31770806 | 2 |
| #31770800 | 2 |
| #31770627 | 2 |
| #474×C269 | 2 |
| #3251 | 269 |