Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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 |
|---|---|---|
| 1. #31771158 | C2 | semidirect |
| 3. #31770966 | C2 | semidirect |
| 4. #31770961 | C2 | semidirect |
| 5. #31770614 | C2 | semidirect |
| 8. M16×Dic269 | C2 | semidirect |
| 9. #419×C269 | C2 | semidirect |
| 12. #22575452 | C22 | semidirect |
| 13. #22575444 | C22 | semidirect |
| 22. #22575377 | C22 | semidirect |
| 25. #22575363 | C22 | semidirect |
| 26. C8×Dic269 | C22 | semidirect |
| 30. #103×C269 | C22 | semidirect |
| 104. C269 | #3140 | semidirect |
| 111. #419 | D269 | semidirect |
| 131. #103 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771158 | 2 |
| C2×#22575442 | 2 |
| #31770966 | 2 |
| #31770961 | 2 |
| #31770614 | 2 |
| #31770611 | 2 |
| #31770609 | 2 |
| M16×Dic269 | 2 |
| #419×C269 | 2 |
| #3140 | 269 |