Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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. #31770622 | C2 | semidirect |
| 3. C2×#22575381 | C2 | semidirect |
| 4. #31770578 | C2 | semidirect |
| 5. #31770375 | C2 | semidirect |
| 6. #31770365 | C2 | semidirect |
| 7. C4×#41×C269 | C2 | semidirect |
| 10. #22575483 | C4 | semidirect |
| 12. #22575478 | C4 | semidirect |
| 33. C2×Dic538 | C2×C4 | semidirect |
| 34. C2×D1076 | C2×C4 | semidirect |
| 44. #16864386 | C2×C4 | semidirect |
| 129. C269 | #1906 | semidirect |
| 132. C4×#41 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771403 | 2 |
| #31770622 | 2 |
| C2×#22575381 | 2 |
| #31770578 | 2 |
| #31770375 | 2 |
| #31770365 | 2 |
| C4×#41×C269 | 2 |
| #1906 | 269 |