Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
596 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 181 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. #31770505 | C2 | semidirect |
| 3. #31770496 | C2 | semidirect |
| 4. #31770488 | C2 | semidirect |
| 5. #31770483 | C2 | semidirect |
| 6. #31770481 | C2 | semidirect |
| 7. #31770468 | C2 | semidirect |
| 8. C4×#16864379 | C2 | semidirect |
| 9. C4×C22⋊C4×C269 | C2 | semidirect |
| 13. #22575427 | C4 | semidirect |
| 38. C2×C22⋊D269 | C2×C4 | semidirect |
| 45. C4⋊Dic269 | C2×C4 | semidirect |
| 52. #16864379 | C2×C4 | semidirect |
| 57. C22×C4×C269 | C2×C4 | semidirect |
| 134. C269 | #2333 | semidirect |
| 144. C4×C22⋊C4 | D269 | semidirect |
| 183. C22×C4 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575427 | 2 |
| #31770505 | 2 |
| #31770496 | 2 |
| #31770488 | 2 |
| #31770483 | 2 |
| #31770481 | 2 |
| #31770468 | 2 |
| C4×#16864379 | 2 |
| C4×C22⋊C4×C269 | 2 |
| #2333 | 269 |