Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
760 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 760 conjugacy classes of subgroups — too many to draw. Only its 165 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. C22×Dic1084 | C2 | semidirect |
| 3. C22×#16864643 | C2 | semidirect |
| 4. C2×#22576139 | C2 | semidirect |
| 5. #31774061 | C2 | direct (N × H) |
| 6. C2×#22576085 | C2 | semidirect |
| 7. C2×#22576082 | C2 | semidirect |
| 8. C2×C22⋊C8×C271 | C2 | semidirect |
| 19. C2×Dic1084 | C22 | semidirect |
| 21. C2×#16864643 | C22 | semidirect |
| 23. #22576139 | C22 | semidirect |
| 27. #22576085 | C22 | semidirect |
| 28. #22576082 | C22 | semidirect |
| 32. C22⋊C8×C271 | C22 | semidirect |
| 130. C2×C271 | #452 | semidirect |
| 135. C271 | C2×#452 | semidirect |
| 144. C2×C22⋊C8 | D271 | semidirect |
| 168. C22⋊C8 | C2×D271 | semidirect |
| 267. C2 | #31774061 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#16864654 | 2 |
| C22×Dic1084 | 2 |
| C22×#16864643 | 2 |
| C2×#22576139 | 2 |
| #31774061 | 2 |
| C2×#22576085 | 2 |
| C2×#22576082 | 2 |
| C2×C22⋊C8×C271 | 2 |
| C2×#452 | 271 |