Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
504 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×#22575475 | C2 | semidirect |
| 2. C2×#22575472 | C2 | semidirect |
| 3. #31771273 | C2 | semidirect |
| 4. #31770980 | C2 | semidirect |
| 5. #31770842 | C2 | semidirect |
| 6. #31770804 | C2 | semidirect |
| 7. #31770751 | C2 | semidirect |
| 8. #31770748 | C2 | semidirect |
| 9. #31770699 | C2 | semidirect |
| 10. C8×C22⋊D269 | C2 | semidirect |
| 11. #466×C269 | C2 | semidirect |
| 56. Dic1076 | D4 | semidirect |
| 134. Dic269 | #135 | semidirect |
| 142. C269 | #3287 | semidirect |
| 149. #466 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575475 | 2 |
| C2×#22575472 | 2 |
| #31771273 | 2 |
| #31770980 | 2 |
| #31770842 | 2 |
| #31770804 | 2 |
| #31770751 | 2 |
| #31770748 | 2 |
| #31770699 | 2 |
| C8×C22⋊D269 | 2 |
| #466×C269 | 2 |
| #3287 | 269 |