Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
340 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 340 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#22575386 | C2 | semidirect |
| 3. C2×#22575377 | C2 | semidirect |
| 5. C2×#22575364 | C2 | semidirect |
| 7. #391×C269 | C2 | semidirect |
| 11. C2×#16864389 | C4 | semidirect |
| 68. #14524130 | C22⋊C4 | semidirect |
| 112. C269 | #1973 | semidirect |
| 119. #391 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864389 | 2 |
| C2×#22575386 | 2 |
| C2×#22575377 | 2 |
| C2×#22575373 | 2 |
| C2×#22575364 | 2 |
| #31770507 | 2 |
| #391×C269 | 2 |
| #1973 | 269 |