Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
176 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 176 conjugacy classes of subgroups — too many to draw. Only its 51 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. #31770951 | C2 | semidirect |
| 2. #31770896 | C2 | semidirect |
| 4. #31770670 | C2 | semidirect |
| 5. #31770355 | C2 | semidirect |
| 6. #31770353 | C2 | semidirect |
| 7. #331×C269 | C2 | semidirect |
| 82. C269 | #1677 | semidirect |
| 90. #331 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770951 | 2 |
| #31770896 | 2 |
| #31770797 | 2 |
| #31770670 | 2 |
| #31770355 | 2 |
| #31770353 | 2 |
| #331×C269 | 2 |
| #1677 | 269 |