Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
342 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 342 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 |
|---|---|---|
| 3. #31771003 | C2 | semidirect |
| 4. #31770944 | C2 | semidirect |
| 5. #31770934 | C2 | semidirect |
| 6. #31770900 | C2 | semidirect |
| 7. #31770890 | C2 | semidirect |
| 8. #31770860 | C2 | semidirect |
| 10. #31770646 | C2 | semidirect |
| 11. C4×Q16×C269 | C2 | semidirect |
| 116. C269 | #3356 | semidirect |
| 126. C4×Q16 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771328 | 2 |
| #31771315 | 2 |
| #31771003 | 2 |
| #31770944 | 2 |
| #31770934 | 2 |
| #31770900 | 2 |
| #31770890 | 2 |
| #31770860 | 2 |
| #31770684 | 2 |
| #31770646 | 2 |
| C4×Q16×C269 | 2 |
| #3356 | 269 |