Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
500 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575483 | C2 | semidirect |
| 3. C2×#22575441 | C2 | semidirect |
| 4. #31770827 | C2 | semidirect |
| 5. #31770820 | C2 | semidirect |
| 6. #31770629 | C2 | semidirect |
| 7. #31770613 | C2 | semidirect |
| 8. #31770609 | C2 | semidirect |
| 9. C4×#41×C269 | C2 | semidirect |
| 14. C2×#16864392 | C22 | semidirect |
| 15. C2×#16864390 | C22 | semidirect |
| 24. C4⋊#14524130 | C22 | semidirect |
| 25. #22575376 | C22 | semidirect |
| 28. C4×Q8×C269 | C22 | semidirect |
| 30. C4×D4×C269 | C22 | semidirect |
| 125. C269 | #3040 | semidirect |
| 130. C4×#41 | D269 | semidirect |
| 150. C4×Q8 | C2×D269 | semidirect |
| 152. C4×D4 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575483 | 2 |
| C2×#22575478 | 2 |
| C2×#22575441 | 2 |
| #31770827 | 2 |
| #31770820 | 2 |
| #31770629 | 2 |
| #31770613 | 2 |
| #31770609 | 2 |
| C4×#41×C269 | 2 |
| #3040 | 269 |