Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
372 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31771233 | C2 | semidirect |
| 2. #31770973 | C2 | semidirect |
| 3. #31770964 | C2 | semidirect |
| 4. #31770959 | C2 | semidirect |
| 5. #31770955 | C2 | semidirect |
| 6. #31770614 | C2 | semidirect |
| 9. C2×#22575377 | C2 | semidirect |
| 10. #31770561 | C2 | semidirect |
| 127. C269 | #3137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771233 | 2 |
| #31770973 | 2 |
| #31770964 | 2 |
| #31770959 | 2 |
| #31770955 | 2 |
| #31770614 | 2 |
| #31770606 | 2 |
| #31770601 | 2 |
| C2×#22575377 | 2 |
| #31770561 | 2 |
| #536×C269 | 2 |
| #3137 | 269 |