Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
416 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 416 conjugacy classes of subgroups — too many to draw. Only its 149 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. #31774238 | C2 | direct (N × H) |
| 3. C2×#22576093 | C2 | semidirect |
| 4. C2×#22576091 | C2 | semidirect |
| 5. C2×#22576083 | C2 | semidirect |
| 6. C2×#22576083 | C2 | semidirect |
| 17. #22576093 | C22 | semidirect |
| 18. #22576091 | C22 | semidirect |
| 19. #22576083 | C22 | semidirect |
| 20. #22576083 | C22 | semidirect |
| 102. C2×C271 | #485 | semidirect |
| 106. C271 | C2×#485 | semidirect |
| 209. C2 | #31774238 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576139 | 2 |
| #31774238 | 2 |
| C2×#22576093 | 2 |
| C2×#22576091 | 2 |
| C2×#22576083 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| C2×#117×C271 | 2 |
| C2×#485 | 271 |