Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
752 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 752 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. C2×#22576191 | C2 | semidirect |
| 3. C22×#16864641 | C2 | semidirect |
| 4. #31774057 | C2 | semidirect |
| 5. #31774047 | C2 | semidirect |
| 6. #31773901 | C2 | semidirect |
| 7. #31773891 | C2 | semidirect |
| 8. #31773864 | C2 | semidirect |
| 9. #536×C271 | C2 | semidirect |
| 20. C2×#16864644 | C22 | semidirect |
| 22. C2×#16864641 | C22 | semidirect |
| 23. C2×#16864641 | C22 | semidirect |
| 24. C2×#16864638 | C22 | semidirect |
| 25. C22×C271⋊C8 | C22 | semidirect |
| 26. #22576083 | C22 | semidirect |
| 27. #22576080 | C22 | semidirect |
| 28. #22576080 | C22 | semidirect |
| 29. C22⋊(C271⋊C8) | C22 | semidirect |
| 31. C22×Q8×C271 | C22 | semidirect |
| 35. C22⋊Q8×C271 | C22 | semidirect |
| 36. #117×C271 | C22 | semidirect |
| 146. C271 | #3009 | semidirect |
| 151. #536 | D271 | semidirect |
| 163. C22×Q8 | C2×D271 | semidirect |
| 178. C22⋊Q8 | C2×D271 | semidirect |
| 179. #117 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576206 | 2 |
| C2×#22576191 | 2 |
| C22×#16864641 | 2 |
| #31774057 | 2 |
| #31774047 | 2 |
| #31773901 | 2 |
| #31773891 | 2 |
| #31773864 | 2 |
| #536×C271 | 2 |
| #3009 | 271 |