Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
390 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 390 conjugacy classes of subgroups — too many to draw. Only its 123 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. C2×Q8×Dic269 | C2 | semidirect |
| 3. #31770933 | C2 | semidirect |
| 5. #31770914 | C2 | semidirect |
| 6. #31770829 | C2 | semidirect |
| 8. Q16×Dic269 | C2 | semidirect |
| 9. #31770690 | C2 | semidirect |
| 10. #31770655 | C2 | semidirect |
| 11. #451×C269 | C2 | semidirect |
| 131. C269 | #3108 | semidirect |
| 139. #451 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771141 | 2 |
| C2×Q8×Dic269 | 2 |
| #31770933 | 2 |
| #31770919 | 2 |
| #31770914 | 2 |
| #31770829 | 2 |
| #31770744 | 2 |
| Q16×Dic269 | 2 |
| #31770690 | 2 |
| #31770655 | 2 |
| #451×C269 | 2 |
| #3108 | 269 |