Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
592 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 592 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×#16864392 | C2 | semidirect |
| 2. C22×#16864391 | C2 | semidirect |
| 4. C2×#22575442 | C2 | semidirect |
| 5. C2×#22575440 | C2 | semidirect |
| 6. #31770986 | C2 | direct (N × H) |
| 7. C2×C8×Dic269 | C2 | semidirect |
| 8. C22×SD16×C269 | C2 | semidirect |
| 12. C2×#16864392 | C22 | semidirect |
| 14. C2×#16864391 | C22 | semidirect |
| 19. #22575442 | C22 | semidirect |
| 21. #22575440 | C22 | semidirect |
| 25. C8×Dic269 | C22 | semidirect |
| 29. C2×SD16×C269 | C22 | semidirect |
| 112. C2×C269 | #495 | semidirect |
| 116. C269 | C2×#495 | semidirect |
| 120. C22×SD16 | D269 | semidirect |
| 135. C2×SD16 | C2×D269 | semidirect |
| 230. C2 | #31770986 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864392 | 2 |
| C22×#16864391 | 2 |
| C22×#16864387 | 2 |
| C2×#22575442 | 2 |
| C2×#22575440 | 2 |
| #31770986 | 2 |
| C2×C8×Dic269 | 2 |
| C22×SD16×C269 | 2 |
| C2×#495 | 269 |