Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
520 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 520 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. #31770509 | C2 | semidirect |
| 3. #31770497 | C2 | semidirect |
| 4. #31770495 | C2 | semidirect |
| 6. #31770479 | C2 | semidirect |
| 7. #31770476 | C2 | semidirect |
| 8. #31770471 | C2 | semidirect |
| 9. #382×C269 | C2 | semidirect |
| 13. #22575441 | C4 | semidirect |
| 35. C2×Dic538 | C2×C4 | semidirect |
| 51. #16864379 | C2×C4 | semidirect |
| 52. #16864379 | C2×C4 | semidirect |
| 61. C42×C269 | C2×C4 | semidirect |
| 127. C269 | #2379 | semidirect |
| 137. #382 | D269 | semidirect |
| 189. C42 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575441 | 2 |
| #31770509 | 2 |
| #31770497 | 2 |
| #31770495 | 2 |
| #31770483 | 2 |
| #31770479 | 2 |
| #31770476 | 2 |
| #31770471 | 2 |
| #382×C269 | 2 |
| #2379 | 269 |