Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
380 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 380 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 |
|---|---|---|
| 3. #31770972 | C2 | semidirect |
| 4. #31770957 | C2 | semidirect |
| 5. #31770956 | C2 | semidirect |
| 6. #31770955 | C2 | semidirect |
| 9. #487×C269 | C2 | semidirect |
| 106. C269 | #3139 | semidirect |
| 114. #487 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771160 | 2 |
| C4⋊Q8×D269 | 2 |
| #31770972 | 2 |
| #31770957 | 2 |
| #31770956 | 2 |
| #31770955 | 2 |
| #31770612 | 2 |
| C4×#16864385 | 2 |
| #487×C269 | 2 |
| #3139 | 269 |