Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
424 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 424 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 |
|---|---|---|
| 2. C4⋊Q8×D269 | C2 | semidirect |
| 3. #31770967 | C2 | semidirect |
| 4. #31770965 | C2 | semidirect |
| 5. #31770964 | C2 | semidirect |
| 6. #31770954 | C2 | semidirect |
| 7. #31770950 | C2 | semidirect |
| 8. #31770605 | C2 | semidirect |
| 9. #31770603 | C2 | semidirect |
| 10. #31770557 | C2 | semidirect |
| 11. #489×C269 | C2 | semidirect |
| 140. C269 | #3141 | semidirect |
| 147. #489 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771154 | 2 |
| C4⋊Q8×D269 | 2 |
| #31770967 | 2 |
| #31770965 | 2 |
| #31770964 | 2 |
| #31770954 | 2 |
| #31770950 | 2 |
| #31770605 | 2 |
| #31770603 | 2 |
| #31770557 | 2 |
| #489×C269 | 2 |
| #3141 | 269 |