Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
500 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 500 conjugacy classes of subgroups — too many to draw. Only its 141 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×#22575486 | C2 | semidirect |
| 3. C2×#22575441 | C2 | semidirect |
| 4. C4×#16864402 | C2 | semidirect |
| 5. #31770828 | C2 | semidirect |
| 6. #31770821 | C2 | semidirect |
| 7. #31770615 | C2 | semidirect |
| 8. #31770611 | C2 | semidirect |
| 9. #423×C269 | C2 | semidirect |
| 15. C2×Dic1076 | C22 | semidirect |
| 17. C2×#16864391 | C22 | semidirect |
| 22. C4×Dic538 | C22 | semidirect |
| 23. C4×D1076 | C22 | semidirect |
| 29. #22575378 | C22 | semidirect |
| 34. C4⋊C8×C269 | C22 | semidirect |
| 125. C269 | #3040 | semidirect |
| 133. #423 | D269 | semidirect |
| 158. C4⋊C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575486 | 2 |
| C2×#22575481 | 2 |
| C2×#22575441 | 2 |
| C4×#16864402 | 2 |
| #31770828 | 2 |
| #31770821 | 2 |
| #31770615 | 2 |
| #31770611 | 2 |
| #423×C269 | 2 |
| #3040 | 269 |