Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
324 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 324 conjugacy classes of subgroups — too many to draw. Only its 85 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 |
|---|---|---|
| 2. #31771372 | C2 | semidirect |
| 3. #31770609 | C2 | semidirect |
| 4. C2×#22575369 | C2 | semidirect |
| 5. #31770375 | C2 | semidirect |
| 6. #31770363 | C2 | semidirect |
| 7. #421×C269 | C2 | semidirect |
| 11. C2×#16864389 | C4 | semidirect |
| 12. C2×#16864387 | C4 | semidirect |
| 112. C269 | #1903 | semidirect |
| 116. #421 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575478 | 2 |
| #31771372 | 2 |
| #31770609 | 2 |
| C2×#22575369 | 2 |
| #31770375 | 2 |
| #31770363 | 2 |
| #421×C269 | 2 |
| #1903 | 269 |