Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575486 | C2 | semidirect |
| 3. #31771181 | C2 | semidirect |
| 4. #31771085 | C2 | semidirect |
| 5. #31770828 | C2 | semidirect |
| 6. #31770821 | C2 | semidirect |
| 7. #31770816 | C2 | semidirect |
| 8. #31770811 | C2 | semidirect |
| 9. #31770607 | C2 | semidirect |
| 10. C2×#22575378 | C2 | semidirect |
| 11. #424×C269 | C2 | semidirect |
| 146. C269 | #3046 | semidirect |
| 156. #424 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| C2×#22575475 | 2 |
| #31771181 | 2 |
| #31771085 | 2 |
| #31770828 | 2 |
| #31770821 | 2 |
| #31770816 | 2 |
| #31770811 | 2 |
| #31770607 | 2 |
| C2×#22575378 | 2 |
| #424×C269 | 2 |
| #3046 | 269 |