Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
740 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 740 conjugacy classes of subgroups — too many to draw. Only its 197 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×D4×Dic269 | C2 | semidirect |
| 3. C2×#22575415 | C2 | semidirect |
| 4. #31770507 | C2 | semidirect |
| 5. #31770482 | C2 | semidirect |
| 6. #31770481 | C2 | semidirect |
| 7. #31770470 | C2 | semidirect |
| 8. #31770451 | C2 | semidirect |
| 9. #390×C269 | C2 | semidirect |
| 14. #22575449 | C4 | semidirect |
| 33. C2×D1076 | C2×C4 | semidirect |
| 36. C2×C22⋊D269 | C2×C4 | semidirect |
| 49. C4×Dic269 | C2×C4 | semidirect |
| 50. C4×Dic269 | D4 | semidirect |
| 54. C2×D4×C269 | C2×C4 | semidirect |
| 123. C269 | #2328 | semidirect |
| 129. #390 | D269 | semidirect |
| 164. C2×D4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575449 | 2 |
| C2×D4×Dic269 | 2 |
| C2×#22575415 | 2 |
| #31770507 | 2 |
| #31770482 | 2 |
| #31770481 | 2 |
| #31770470 | 2 |
| #31770451 | 2 |
| #390×C269 | 2 |
| #2328 | 269 |