Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
444 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 444 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 |
|---|---|---|
| 1. #31771422 | C2 | semidirect |
| 2. #31771419 | C2 | semidirect |
| 3. #31770985 | C2 | semidirect |
| 4. #31770881 | C2 | semidirect |
| 5. #31770880 | C2 | semidirect |
| 6. #31770789 | C2 | semidirect |
| 7. #31770723 | C2 | semidirect |
| 8. #443×C269 | C2 | semidirect |
| 99. C269 | #3293 | semidirect |
| 108. #443 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771422 | 2 |
| #31771419 | 2 |
| #31770985 | 2 |
| #31770881 | 2 |
| #31770880 | 2 |
| #31770789 | 2 |
| #31770723 | 2 |
| #443×C269 | 2 |
| #3293 | 269 |