Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#22575472 | C2 | semidirect |
| 2. #31771254 | C2 | semidirect |
| 3. #31770983 | C2 | semidirect |
| 4. #31770846 | C2 | semidirect |
| 5. #31770843 | C2 | semidirect |
| 6. #31770808 | C2 | semidirect |
| 7. #31770767 | C2 | semidirect |
| 8. #31770764 | C2 | semidirect |
| 9. D8×Dic269 | C2 | semidirect |
| 10. C8×C22⋊D269 | C2 | semidirect |
| 11. C2×#135×C269 | C2 | semidirect |
| 76. D8×C269 | D4 | semidirect |
| 129. Dic269 | #135 | semidirect |
| 136. C269 | #3283 | semidirect |
| 139. C2×#135 | D269 | semidirect |
| 198. D8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575472 | 2 |
| #31771254 | 2 |
| #31770983 | 2 |
| #31770846 | 2 |
| #31770843 | 2 |
| #31770808 | 2 |
| #31770767 | 2 |
| #31770764 | 2 |
| D8×Dic269 | 2 |
| C8×C22⋊D269 | 2 |
| C2×#135×C269 | 2 |
| #3283 | 269 |