Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 2. #31770943 | C2 | semidirect |
| 3. #31770897 | C2 | semidirect |
| 4. #31770892 | C2 | semidirect |
| 5. #31770812 | C2 | semidirect |
| 6. #31770807 | C2 | semidirect |
| 8. #31770710 | C2 | semidirect |
| 9. #31770703 | C2 | semidirect |
| 10. #31770662 | C2 | semidirect |
| 11. #533×C269 | C2 | semidirect |
| 136. C269 | #3116 | semidirect |
| 138. #533 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×#16864402 | 2 |
| #31770943 | 2 |
| #31770897 | 2 |
| #31770892 | 2 |
| #31770812 | 2 |
| #31770807 | 2 |
| #31770765 | 2 |
| #31770710 | 2 |
| #31770703 | 2 |
| #31770662 | 2 |
| #533×C269 | 2 |
| #3116 | 269 |