Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
476 conjugacy classes of subgroups; only the 213 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 213 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 |
|---|---|---|
| 3. #31770648 | C2 | semidirect |
| 4. #31770646 | C2 | semidirect |
| 5. #31770640 | C2 | semidirect |
| 6. C2×#22575385 | C2 | semidirect |
| 7. #106×D269 | C2 | semidirect |
| 8. #427×C269 | C2 | semidirect |
| 10. #22575459 | C4 | semidirect |
| 37. #16864386 | C2×C4 | semidirect |
| 38. #16864385 | C2×C4 | semidirect |
| 40. C8×D269 | C2×C4 | semidirect |
| 47. C2×C8×C269 | C2×C4 | semidirect |
| 90. C269 | #2912 | semidirect |
| 97. #427 | D269 | semidirect |
| 133. C2×C8 | C4×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575459 | 2 |
| #31771085 | 2 |
| #31770648 | 2 |
| #31770646 | 2 |
| #31770640 | 2 |
| C2×#22575385 | 2 |
| #106×D269 | 2 |
| #427×C269 | 2 |
| #2912 | 269 |