Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
444 conjugacy classes of subgroups; only the 129 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 129 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. #31771162 | C2 | semidirect |
| 3. #31770941 | C2 | semidirect |
| 4. #31770886 | C2 | semidirect |
| 5. #31770811 | C2 | semidirect |
| 7. #31770707 | C2 | semidirect |
| 8. #432×C269 | C2 | semidirect |
| 12. #22575453 | C22 | semidirect |
| 13. #22575453 | C22 | semidirect |
| 18. C4×Dic538 | C22 | semidirect |
| 26. #22575387 | C22 | semidirect |
| 27. #22575378 | C22 | semidirect |
| 30. C4⋊C8×C269 | C22 | semidirect |
| 32. #97×C269 | C22 | semidirect |
| 112. C269 | #3110 | semidirect |
| 121. #432 | D269 | semidirect |
| 141. C4⋊C8 | C2×D269 | semidirect |
| 145. #97 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771162 | 2 |
| C2×C4×D1076 | 2 |
| #31770941 | 2 |
| #31770886 | 2 |
| #31770811 | 2 |
| #31770758 | 2 |
| #31770707 | 2 |
| #432×C269 | 2 |
| #3110 | 269 |