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×#16864644 | C2 | semidirect |
| 3. C22×#16864641 | C2 | semidirect |
| 4. #31774057 | C2 | direct (N × H) |
| 5. C2×#22576083 | C2 | semidirect |
| 6. C2×#22576080 | C2 | semidirect |
| 7. C2×C22⋊(C271⋊C8) | C2 | semidirect |
| 8. C2×C22⋊Q8×C271 | C2 | semidirect |
| 18. C2×#16864644 | C22 | semidirect |
| 20. C2×#16864641 | C22 | semidirect |
| 23. #22576083 | C22 | semidirect |
| 24. #22576080 | C22 | semidirect |
| 25. C22⋊(C271⋊C8) | C22 | semidirect |
| 29. C22⋊Q8×C271 | C22 | semidirect |
| 130. C2×C271 | #452 | semidirect |
| 135. C271 | C2×#452 | semidirect |
| 140. C2×C22⋊Q8 | D271 | semidirect |
| 162. C22⋊Q8 | C2×D271 | semidirect |
| 267. C2 | #31774057 | 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×#16864644 | 2 |
| C22×#16864641 | 2 |
| #31774057 | 2 |
| C2×#22576083 | 2 |
| C2×#22576080 | 2 |
| C2×C22⋊(C271⋊C8) | 2 |
| C2×C22⋊Q8×C271 | 2 |
| C2×#452 | 271 |