Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
532 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 532 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 |
|---|---|---|
| 1. C2×#22575484 | C2 | semidirect |
| 2. C2×#22575483 | C2 | semidirect |
| 4. C22×#16864392 | C2 | semidirect |
| 5. #31771181 | C2 | semidirect |
| 6. #31771000 | C2 | semidirect |
| 7. #31770997 | C2 | semidirect |
| 8. #31770987 | C2 | semidirect |
| 9. #31770984 | C2 | semidirect |
| 10. #31770561 | C2 | semidirect |
| 11. #536×C269 | C2 | semidirect |
| 143. C269 | #3156 | semidirect |
| 150. #536 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| C2×#22575483 | 2 |
| C2×#22575473 | 2 |
| C22×#16864392 | 2 |
| #31771181 | 2 |
| #31771000 | 2 |
| #31770997 | 2 |
| #31770987 | 2 |
| #31770984 | 2 |
| #31770561 | 2 |
| #536×C269 | 2 |
| #3156 | 269 |