Finite Group DatabasebetaFinite Group DatabasebetaOrder 34432.
216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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×Dic2152 | C2 | semidirect |
| 3. C2×#22575399 | C2 | semidirect |
| 5. #31770408 | C2 | semidirect |
| 7. #358×C269 | C2 | semidirect |
| 70. C2×D269 | Q32 | semidirect |
| 82. C269 | #2188 | semidirect |
| 89. #358 | D269 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D269 | 2 |
| C2×Dic2152 | 2 |
| C2×#22575399 | 2 |
| #31770847 | 2 |
| #31770408 | 2 |
| #31770384 | 2 |
| #358×C269 | 2 |
| #2188 | 269 |