Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
338 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 123 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. Q8×Dic538 | C2 | semidirect |
| 4. #31770956 | C2 | semidirect |
| 6. #31770891 | C2 | semidirect |
| 8. #31770816 | C2 | semidirect |
| 9. #31770713 | C2 | semidirect |
| 11. #446×C269 | C2 | semidirect |
| 116. C269 | #3369 | semidirect |
| 126. #446 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic538 | 2 |
| #31771328 | 2 |
| #31770965 | 2 |
| #31770956 | 2 |
| #31770896 | 2 |
| #31770891 | 2 |
| #31770828 | 2 |
| #31770816 | 2 |
| #31770713 | 2 |
| C4×#16864391 | 2 |
| #446×C269 | 2 |
| #3369 | 269 |