Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
232 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 232 conjugacy classes of subgroups — too many to draw. Only its 81 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. #31770647 | C2 | semidirect |
| 4. #31770563 | C2 | semidirect |
| 5. #31770373 | C2 | semidirect |
| 6. #31770369 | C2 | semidirect |
| 23. #100×C269 | C4 | semidirect |
| 100. C269 | #1931 | semidirect |
| 122. #100 | Dic269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31770647 | 2 |
| #31770610 | 2 |
| C2×#22575374 | 2 |
| #31770563 | 2 |
| #31770373 | 2 |
| #31770369 | 2 |
| C2×#100×C269 | 2 |
| #1931 | 269 |