Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
336 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 115 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. #31771330 | C2 | semidirect |
| 4. #31770910 | C2 | semidirect |
| 7. #31770812 | C2 | semidirect |
| 8. C8×Dic538 | C2 | semidirect |
| 9. #31770697 | C2 | semidirect |
| 11. #487×C269 | C2 | semidirect |
| 115. C269 | #3364 | semidirect |
| 120. #487 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771330 | 2 |
| #31771329 | 2 |
| #31770961 | 2 |
| #31770910 | 2 |
| #31770882 | 2 |
| #31770830 | 2 |
| #31770812 | 2 |
| C8×Dic538 | 2 |
| #31770697 | 2 |
| C4×#16864391 | 2 |
| #487×C269 | 2 |
| #3364 | 269 |