Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
576 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 173 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. #31770497 | C2 | semidirect |
| 4. #31770488 | C2 | semidirect |
| 5. #31770483 | C2 | semidirect |
| 6. #31770481 | C2 | semidirect |
| 7. #31770479 | C2 | semidirect |
| 8. #31770465 | C2 | semidirect |
| 9. #381×C269 | C2 | semidirect |
| 13. #22575427 | C4 | semidirect |
| 37. C2×C22⋊D269 | C2×C4 | semidirect |
| 45. C4⋊Dic269 | C2×C4 | semidirect |
| 52. #16864379 | C2×C4 | semidirect |
| 56. C22×C4×C269 | C2×C4 | semidirect |
| 129. C269 | #2377 | semidirect |
| 138. #381 | D269 | semidirect |
| 176. 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 |
| #31770497 | 2 |
| #31770488 | 2 |
| #31770483 | 2 |
| #31770481 | 2 |
| #31770479 | 2 |
| #31770465 | 2 |
| #381×C269 | 2 |
| #2377 | 269 |