Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
712 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 149 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×#22575501 | C2 | semidirect |
| 2. C2×#22575473 | C2 | semidirect |
| 3. #31771183 | C2 | semidirect |
| 4. #31770766 | C2 | semidirect |
| 5. #31770759 | C2 | semidirect |
| 6. #31770749 | C2 | semidirect |
| 7. #31770742 | C2 | semidirect |
| 8. #31770607 | C2 | semidirect |
| 9. C2×#22575377 | C2 | semidirect |
| 10. #31770573 | C2 | semidirect |
| 11. C2×#137×C269 | C2 | semidirect |
| 52. #16864402 | D4 | semidirect |
| 86. C2×Q8×C269 | D4 | semidirect |
| 169. C269 | #3013 | semidirect |
| 172. C2×#137 | D269 | semidirect |
| 233. C2×Q8 | C22⋊D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575501 | 2 |
| C2×#22575473 | 2 |
| #31771183 | 2 |
| #31770766 | 2 |
| #31770759 | 2 |
| #31770749 | 2 |
| #31770742 | 2 |
| #31770607 | 2 |
| C2×#22575377 | 2 |
| #31770573 | 2 |
| C2×#137×C269 | 2 |
| #3013 | 269 |