Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
348 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 348 conjugacy classes of subgroups — too many to draw. Only its 121 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 |
|---|---|---|
| 2. #31770899 | C2 | semidirect |
| 3. #31770898 | C2 | semidirect |
| 6. #31770814 | C2 | semidirect |
| 7. #31770813 | C2 | semidirect |
| 70. C2×Dic269 | Q16 | semidirect |
| 102. C269 | #3249 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771157 | 2 |
| #31770899 | 2 |
| #31770898 | 2 |
| #31770846 | 2 |
| #31770844 | 2 |
| #31770814 | 2 |
| #31770813 | 2 |
| C2×#22575382 | 2 |
| #467×C269 | 2 |
| #3249 | 269 |