Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
392 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 133 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. #31771162 | C2 | semidirect |
| 3. #31770974 | C2 | semidirect |
| 4. #31770970 | C2 | semidirect |
| 5. #31770965 | C2 | semidirect |
| 6. #31770602 | C2 | semidirect |
| 7. C2×#97×C269 | C2 | semidirect |
| 78. C269 | #3135 | semidirect |
| 86. C2×#97 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| #31771155 | 2 |
| #31770974 | 2 |
| #31770970 | 2 |
| #31770965 | 2 |
| #31770602 | 2 |
| C2×#97×C269 | 2 |
| #3135 | 269 |