Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
210 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 210 conjugacy classes of subgroups — too many to draw. Only its 47 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. #31771419 | C2 | semidirect |
| 2. C2×#22575397 | C2 | semidirect |
| 3. #31770872 | C2 | semidirect |
| 4. #31770422 | C2 | semidirect |
| 5. #31770412 | C2 | semidirect |
| 6. #31770390 | C2 | semidirect |
| 7. #509×C269 | C2 | semidirect |
| 90. C269 | #2193 | semidirect |
| 93. #509 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771419 | 2 |
| C2×#22575397 | 2 |
| #31770872 | 2 |
| #31770422 | 2 |
| #31770412 | 2 |
| #31770390 | 2 |
| #509×C269 | 2 |
| #2193 | 269 |