Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 189 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 |
|---|---|---|
| 3. #31770492 | C2 | semidirect |
| 4. #31770475 | C2 | semidirect |
| 6. C4⋊C4×Dic269 | C2 | semidirect |
| 7. #382×C269 | C2 | semidirect |
| 9. #22575410 | C4 | semidirect |
| 88. C269 | #2314 | semidirect |
| 94. #382 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575410 | 2 |
| #31770497 | 2 |
| #31770492 | 2 |
| #31770475 | 2 |
| #31770462 | 2 |
| C4⋊C4×Dic269 | 2 |
| #382×C269 | 2 |
| #2314 | 269 |