Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
532 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 137 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. C2×#22575485 | C2 | semidirect |
| 3. C2×Q16×D269 | C2 | semidirect |
| 4. #31771180 | C2 | semidirect |
| 5. #31770998 | C2 | semidirect |
| 6. #31770997 | C2 | semidirect |
| 7. #31770990 | C2 | semidirect |
| 8. #31770989 | C2 | semidirect |
| 9. #31770983 | C2 | semidirect |
| 10. #31770559 | C2 | semidirect |
| 11. #494×C269 | C2 | semidirect |
| 121. C269 | #3156 | semidirect |
| 132. #494 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575485 | 2 |
| C2×#22575476 | 2 |
| C2×Q16×D269 | 2 |
| #31771180 | 2 |
| #31770998 | 2 |
| #31770997 | 2 |
| #31770990 | 2 |
| #31770989 | 2 |
| #31770983 | 2 |
| #31770559 | 2 |
| #494×C269 | 2 |
| #3156 | 269 |