Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
754 conjugacy classes of subgroups; only the 169 normal subgroups are shown.
This group has 754 conjugacy classes of subgroups — too many to draw. Only its 169 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 |
| 2. C2×#22575432 | C2 | semidirect |
| 3. #31770767 | C2 | semidirect |
| 4. #31770761 | C2 | semidirect |
| 5. #31770756 | C2 | semidirect |
| 6. #31770606 | C2 | semidirect |
| 7. #31770569 | C2 | semidirect |
| 9. C22×Dic538 | C22 | semidirect |
| 11. C2×#16864392 | C22 | semidirect |
| 12. C2×#16864390 | C22 | semidirect |
| 13. C2×#16864386 | C22 | semidirect |
| 17. #22575432 | C22 | semidirect |
| 18. C2×C4⋊Dic269 | C22 | semidirect |
| 21. #22575377 | C22 | semidirect |
| 22. #22575374 | C22 | semidirect |
| 24. C22⋊#14524130 | C22 | semidirect |
| 130. C22×C269 | #137 | semidirect |
| 146. C269 | #3007 | semidirect |
| 277. C22 | #22575483 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575483 | 2 |
| C2×#22575432 | 2 |
| #31770767 | 2 |
| #31770761 | 2 |
| #31770756 | 2 |
| #31770606 | 2 |
| #31770569 | 2 |
| C22×#41×C269 | 2 |
| #3007 | 269 |