Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
484 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 484 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 |
|---|---|---|
| 1. C2×#22575476 | C2 | semidirect |
| 2. C2×#22575475 | C2 | semidirect |
| 3. #31771257 | C2 | semidirect |
| 4. #31770983 | C2 | semidirect |
| 5. #31770847 | C2 | semidirect |
| 6. #31770809 | C2 | semidirect |
| 7. #31770770 | C2 | semidirect |
| 8. #31770765 | C2 | semidirect |
| 9. #31770687 | C2 | semidirect |
| 10. C8×C22⋊D269 | C2 | semidirect |
| 11. #467×C269 | C2 | semidirect |
| 58. D2152 | D4 | semidirect |
| 129. Dic269 | #135 | semidirect |
| 136. C269 | #3283 | semidirect |
| 143. #467 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C2×#22575475 | 2 |
| #31771257 | 2 |
| #31770983 | 2 |
| #31770847 | 2 |
| #31770809 | 2 |
| #31770770 | 2 |
| #31770765 | 2 |
| #31770687 | 2 |
| C8×C22⋊D269 | 2 |
| #467×C269 | 2 |
| #3283 | 269 |