Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
220 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 220 conjugacy classes of subgroups — too many to draw. Only its 51 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×#22575399 | C2 | semidirect |
| 3. C2×#22575398 | C2 | semidirect |
| 4. #31770847 | C2 | semidirect |
| 5. #31770405 | C2 | semidirect |
| 6. #31770384 | C2 | semidirect |
| 7. #358×C269 | C2 | semidirect |
| 85. C269 | #2189 | semidirect |
| 91. #358 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22575476 | 2 |
| C2×#22575399 | 2 |
| C2×#22575398 | 2 |
| #31770847 | 2 |
| #31770405 | 2 |
| #31770384 | 2 |
| #358×C269 | 2 |
| #2189 | 269 |