Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
376 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 376 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. #31771236 | C2 | semidirect |
| 3. #31770911 | C2 | semidirect |
| 4. #31770908 | C2 | semidirect |
| 5. #31770899 | C2 | semidirect |
| 6. #31770884 | C2 | semidirect |
| 7. #31770645 | C2 | semidirect |
| 8. #31770631 | C2 | semidirect |
| 11. C2×#107×C269 | C2 | semidirect |
| 42. #16864402 | Q8 | semidirect |
| 123. C269 | #3083 | semidirect |
| 132. C2×#107 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771236 | 2 |
| #31771086 | 2 |
| #31770911 | 2 |
| #31770908 | 2 |
| #31770899 | 2 |
| #31770884 | 2 |
| #31770645 | 2 |
| #31770631 | 2 |
| #31770604 | 2 |
| #31770602 | 2 |
| C2×#107×C269 | 2 |
| #3083 | 269 |