Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771153 | C2 | semidirect |
| 2. #31771152 | C2 | semidirect |
| 3. #31770896 | C2 | semidirect |
| 4. #31770895 | C2 | semidirect |
| 5. #31770893 | C2 | semidirect |
| 6. #31770857 | C2 | semidirect |
| 7. #31770855 | C2 | semidirect |
| 8. #31770798 | C2 | semidirect |
| 9. #31770797 | C2 | semidirect |
| 10. #31770627 | C2 | semidirect |
| 11. #459×C269 | C2 | semidirect |
| 150. C269 | #3253 | semidirect |
| 161. #459 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771153 | 2 |
| #31771152 | 2 |
| #31770896 | 2 |
| #31770895 | 2 |
| #31770893 | 2 |
| #31770857 | 2 |
| #31770855 | 2 |
| #31770798 | 2 |
| #31770797 | 2 |
| #31770627 | 2 |
| #459×C269 | 2 |
| #3253 | 269 |