Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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 |
|---|---|---|
| 1. #31771341 | C2 | semidirect |
| 2. #31771316 | C2 | semidirect |
| 3. #31770958 | C2 | semidirect |
| 4. #31770907 | C2 | semidirect |
| 5. #31770897 | C2 | semidirect |
| 6. #31770819 | C2 | semidirect |
| 8. C8×Dic538 | C2 | semidirect |
| 9. C4×#16864391 | C2 | semidirect |
| 10. #31770685 | C2 | semidirect |
| 11. #486×C269 | C2 | semidirect |
| 122. C269 | #3361 | semidirect |
| 127. #486 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771341 | 2 |
| #31771316 | 2 |
| #31770958 | 2 |
| #31770907 | 2 |
| #31770897 | 2 |
| #31770819 | 2 |
| #31770797 | 2 |
| C8×Dic538 | 2 |
| C4×#16864391 | 2 |
| #31770685 | 2 |
| #486×C269 | 2 |
| #3361 | 269 |