Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
374 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 374 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. #31771328 | C2 | semidirect |
| 3. #31771008 | C2 | semidirect |
| 4. #31770939 | C2 | semidirect |
| 5. #31770931 | C2 | semidirect |
| 6. #31770886 | C2 | semidirect |
| 7. #31770854 | C2 | semidirect |
| 8. C4×#16864389 | C2 | semidirect |
| 9. #31770682 | C2 | semidirect |
| 10. #31770644 | C2 | semidirect |
| 11. #475×C269 | C2 | semidirect |
| 89. #14524130 | #41 | semidirect |
| 122. C269 | #3353 | semidirect |
| 129. #475 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| #31771258 | 2 |
| #31771008 | 2 |
| #31770939 | 2 |
| #31770931 | 2 |
| #31770886 | 2 |
| #31770854 | 2 |
| C4×#16864389 | 2 |
| #31770682 | 2 |
| #31770644 | 2 |
| #475×C269 | 2 |
| #3353 | 269 |