Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
390 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 390 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 |
|---|---|---|
| 2. #31770935 | C2 | semidirect |
| 4. #31770912 | C2 | semidirect |
| 5. #31770827 | C2 | semidirect |
| 6. #31770761 | C2 | semidirect |
| 8. C4×#16864392 | C2 | semidirect |
| 9. C4×#16864389 | C2 | semidirect |
| 10. #31770658 | C2 | semidirect |
| 11. C2×C4×Q8×C269 | C2 | semidirect |
| 131. C269 | #3108 | semidirect |
| 134. C2×C4×Q8 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771139 | 2 |
| #31770935 | 2 |
| #31770918 | 2 |
| #31770912 | 2 |
| #31770827 | 2 |
| #31770761 | 2 |
| #31770744 | 2 |
| C4×#16864392 | 2 |
| C4×#16864389 | 2 |
| #31770658 | 2 |
| C2×C4×Q8×C269 | 2 |
| #3108 | 269 |