Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
612 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 612 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×#22575418 | C2 | semidirect |
| 4. #31770510 | C2 | semidirect |
| 6. #31770495 | C2 | semidirect |
| 7. #31770476 | C2 | semidirect |
| 8. #31770451 | C2 | semidirect |
| 9. #384×C269 | C2 | semidirect |
| 13. #22575441 | C4 | semidirect |
| 33. C2×Dic538 | C2×C4 | semidirect |
| 46. #16864379 | C2×C4 | semidirect |
| 57. C42×C269 | C2×C4 | semidirect |
| 111. C269 | #2326 | semidirect |
| 120. #384 | D269 | semidirect |
| 169. 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 |
| C2×#22575418 | 2 |
| C2×#22575415 | 2 |
| #31770510 | 2 |
| #31770506 | 2 |
| #31770495 | 2 |
| #31770476 | 2 |
| #31770451 | 2 |
| #384×C269 | 2 |
| #2326 | 269 |