Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
240 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 240 conjugacy classes of subgroups — too many to draw. Only its 75 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 |
|---|---|---|
| 4. #31770352 | C2 | semidirect |
| 5. #31770351 | C2 | semidirect |
| 6. #31770350 | C2 | semidirect |
| 7. #332×C269 | C2 | semidirect |
| 91. C269 | #1549 | semidirect |
| 99. #332 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×D269 | 2 |
| #31770657 | 2 |
| #31770627 | 2 |
| #31770352 | 2 |
| #31770351 | 2 |
| #31770350 | 2 |
| #332×C269 | 2 |
| #1549 | 269 |