Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
344 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 344 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×Dic271⋊C8 | C2 | semidirect |
| 3. C2×#22576085 | C2 | semidirect |
| 4. C2×#22576083 | C2 | semidirect |
| 6. C4⋊C4×Dic271 | C2 | semidirect |
| 11. #22576147 | C4 | semidirect |
| 130. C271 | #1983 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576147 | 2 |
| C2×Dic271⋊C8 | 2 |
| C2×#22576085 | 2 |
| C2×#22576083 | 2 |
| C2×#22576081 | 2 |
| C4⋊C4×Dic271 | 2 |
| C2×#102×C271 | 2 |
| #1983 | 271 |