Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
704 conjugacy classes of subgroups; only the 161 normal subgroups are shown.
This group has 704 conjugacy classes of subgroups — too many to draw. Only its 161 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. #31771176 | C2 | semidirect |
| 3. #31770788 | C2 | semidirect |
| 4. #31770783 | C2 | semidirect |
| 5. #31770622 | C2 | semidirect |
| 6. #31770589 | C2 | semidirect |
| 8. C22×Dic538 | C22 | semidirect |
| 10. #22575483 | C22 | semidirect |
| 13. C2×#16864386 | C22 | semidirect |
| 14. #22575451 | C22 | semidirect |
| 15. #22575440 | C22 | semidirect |
| 18. #22575412 | C22 | semidirect |
| 19. #22575380 | C22 | semidirect |
| 20. #22575372 | C22 | semidirect |
| 21. #22575370 | C22 | semidirect |
| 129. C269 | #3022 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575483 | 2 |
| #31771176 | 2 |
| #31770788 | 2 |
| #31770783 | 2 |
| #31770622 | 2 |
| #31770589 | 2 |
| #585×C269 | 2 |
| #3022 | 269 |