Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
472 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 472 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×#22575484 | C2 | semidirect |
| 2. C2×#22575460 | C2 | semidirect |
| 4. #31770861 | C2 | semidirect |
| 5. #31770853 | C2 | semidirect |
| 6. #31770844 | C2 | semidirect |
| 7. #31770836 | C2 | semidirect |
| 8. #31770648 | C2 | semidirect |
| 9. #31770599 | C2 | semidirect |
| 10. C2×#22575377 | C2 | semidirect |
| 11. #536×C269 | C2 | semidirect |
| 54. #16864386 | D4 | semidirect |
| 143. C269 | #3063 | semidirect |
| 148. #536 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575484 | 2 |
| C2×#22575460 | 2 |
| #31771183 | 2 |
| #31770861 | 2 |
| #31770853 | 2 |
| #31770844 | 2 |
| #31770836 | 2 |
| #31770648 | 2 |
| #31770599 | 2 |
| C2×#22575377 | 2 |
| #536×C269 | 2 |
| #3063 | 269 |