Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
458 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 458 conjugacy classes of subgroups — too many to draw. Only its 141 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. #31771083 | C2 | semidirect |
| 4. #31770829 | C2 | semidirect |
| 5. #31770813 | C2 | semidirect |
| 6. #31770631 | C2 | semidirect |
| 7. #31770614 | C2 | semidirect |
| 9. C22×Q16×C269 | C2 | semidirect |
| 111. C269 | #3044 | semidirect |
| 114. C22×Q16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| #31771179 | 2 |
| #31771083 | 2 |
| #31770829 | 2 |
| #31770813 | 2 |
| #31770631 | 2 |
| #31770614 | 2 |
| #31770602 | 2 |
| C22×Q16×C269 | 2 |
| #3044 | 269 |