Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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. #31771341 | C2 | semidirect |
| 2. #31771312 | C2 | semidirect |
| 3. #31770958 | C2 | semidirect |
| 4. #31770951 | C2 | semidirect |
| 5. #31770903 | C2 | semidirect |
| 6. #31770901 | C2 | semidirect |
| 7. #31770818 | C2 | semidirect |
| 8. #31770729 | C2 | semidirect |
| 9. C4×#16864390 | C2 | semidirect |
| 10. D8×Dic269 | C2 | semidirect |
| 122. C269 | #3361 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771341 | 2 |
| #31771312 | 2 |
| #31770958 | 2 |
| #31770951 | 2 |
| #31770903 | 2 |
| #31770901 | 2 |
| #31770818 | 2 |
| #31770729 | 2 |
| C4×#16864390 | 2 |
| D8×Dic269 | 2 |
| #459×C269 | 2 |
| #3361 | 269 |