Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
386 conjugacy classes of subgroups; only the 123 normal subgroups are shown.
This group has 386 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. #31771325 | C2 | semidirect |
| 3. #31770956 | C2 | semidirect |
| 4. #31770947 | C2 | semidirect |
| 5. #31770886 | C2 | semidirect |
| 6. #31770846 | C2 | semidirect |
| 7. #31770816 | C2 | semidirect |
| 8. #31770769 | C2 | semidirect |
| 9. C4×#16864391 | C2 | semidirect |
| 10. #31770602 | C2 | semidirect |
| 11. C8×D4×C269 | C2 | semidirect |
| 125. C269 | #3302 | semidirect |
| 136. C8×D4 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31771325 | 2 |
| #31771260 | 2 |
| #31770956 | 2 |
| #31770947 | 2 |
| #31770886 | 2 |
| #31770846 | 2 |
| #31770816 | 2 |
| #31770769 | 2 |
| C4×#16864391 | 2 |
| #31770602 | 2 |
| C8×D4×C269 | 2 |
| #3302 | 269 |