Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
446 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22575486 | C2 | semidirect |
| 3. C2×#22575483 | C2 | semidirect |
| 4. #31770880 | C2 | semidirect |
| 5. #31770868 | C2 | semidirect |
| 6. #31770654 | C2 | semidirect |
| 7. #31770587 | C2 | semidirect |
| 8. C2×#22575371 | C2 | semidirect |
| 9. #568×C269 | C2 | semidirect |
| 21. C2×Dic1076 | C22 | semidirect |
| 23. C2×#16864391 | C22 | semidirect |
| 27. #22575389 | C22 | semidirect |
| 28. #22575371 | C22 | semidirect |
| 29. #22575371 | C22 | semidirect |
| 30. #22575369 | C22 | semidirect |
| 142. C269 | #3069 | semidirect |
| 147. #568 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771403 | 2 |
| C2×#22575486 | 2 |
| C2×#22575483 | 2 |
| #31770880 | 2 |
| #31770868 | 2 |
| #31770654 | 2 |
| #31770587 | 2 |
| C2×#22575371 | 2 |
| #568×C269 | 2 |
| #3069 | 269 |