Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
500 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 500 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 |
|---|---|---|
| 1. C2×#22575484 | C2 | semidirect |
| 3. C2×#22575442 | C2 | semidirect |
| 4. #31771073 | C2 | semidirect |
| 5. #31770830 | C2 | semidirect |
| 6. #31770823 | C2 | semidirect |
| 7. #31770628 | C2 | semidirect |
| 8. #31770609 | C2 | semidirect |
| 9. #419×C269 | C2 | semidirect |
| 14. C2×#16864392 | C22 | semidirect |
| 16. C2×#16864389 | C22 | semidirect |
| 22. #22575418 | C22 | semidirect |
| 23. #22575415 | C22 | semidirect |
| 29. #22575382 | C22 | semidirect |
| 34. #103×C269 | C22 | semidirect |
| 125. C269 | #3040 | semidirect |
| 134. #419 | D269 | semidirect |
| 159. #103 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| C2×#22575481 | 2 |
| C2×#22575442 | 2 |
| #31771073 | 2 |
| #31770830 | 2 |
| #31770823 | 2 |
| #31770628 | 2 |
| #31770609 | 2 |
| #419×C269 | 2 |
| #3040 | 269 |