Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
346 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 346 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 2. C4×C22⋊Dic269 | C2 | semidirect |
| 3. #31770340 | C2 | semidirect |
| 4. #407×C269 | C2 | semidirect |
| 5. C22×D1076 | C4 | semidirect |
| 9. #22575427 | C4 | semidirect |
| 11. C2×C4⋊Dic269 | C4 | semidirect |
| 15. #22575360 | C22 | semidirect |
| 19. C22⋊C8×C269 | C22 | semidirect |
| 103. C269 | #1507 | semidirect |
| 106. #407 | D269 | semidirect |
| 122. C22⋊C8 | C2×D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575427 | 2 |
| C4×C22⋊Dic269 | 2 |
| #31770340 | 2 |
| #407×C269 | 2 |
| #1507 | 269 |