Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22575484 | C2 | semidirect |
| 3. #31771179 | C2 | semidirect |
| 4. #31770766 | C2 | semidirect |
| 5. #31770759 | C2 | semidirect |
| 6. #31770614 | C2 | semidirect |
| 7. #31770602 | C2 | semidirect |
| 8. #31770571 | C2 | semidirect |
| 9. C22×Q16×C269 | C2 | semidirect |
| 140. C269 | #3011 | semidirect |
| 144. C22×Q16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575501 | 2 |
| C2×#22575484 | 2 |
| #31771179 | 2 |
| #31770766 | 2 |
| #31770759 | 2 |
| #31770614 | 2 |
| #31770602 | 2 |
| #31770571 | 2 |
| C22×Q16×C269 | 2 |
| #3011 | 269 |