Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 117 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. #125×D269 | C2 | semidirect |
| 3. #31770972 | C2 | semidirect |
| 4. #31770968 | C2 | semidirect |
| 5. #31770962 | C2 | semidirect |
| 6. #31770960 | C2 | semidirect |
| 7. #31770959 | C2 | semidirect |
| 8. #31770605 | C2 | semidirect |
| 9. #31770603 | C2 | semidirect |
| 10. C4×#16864385 | C2 | semidirect |
| 11. #488×C269 | C2 | semidirect |
| 114. C269 | #3142 | semidirect |
| 123. #488 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771154 | 2 |
| #125×D269 | 2 |
| #31770972 | 2 |
| #31770968 | 2 |
| #31770962 | 2 |
| #31770960 | 2 |
| #31770959 | 2 |
| #31770605 | 2 |
| #31770603 | 2 |
| C4×#16864385 | 2 |
| #488×C269 | 2 |
| #3142 | 269 |