Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
548 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 153 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 |
|---|---|---|
| 1. C2×#22576186 | C2 | semidirect |
| 2. #31774447 | C2 | semidirect |
| 3. #31774112 | C2 | semidirect |
| 4. #31774102 | C2 | semidirect |
| 5. #31774092 | C2 | semidirect |
| 6. #31773921 | C2 | semidirect |
| 7. #31773896 | C2 | semidirect |
| 8. C2×C4×D4×C271 | C2 | semidirect |
| 14. #22576160 | C22 | semidirect |
| 15. #22576157 | C22 | semidirect |
| 16. #22576148 | C22 | semidirect |
| 21. C4⋊(C271⋊C8) | C22 | semidirect |
| 22. C4⋊(C271⋊C8) | C22 | semidirect |
| 23. #22576083 | C22 | semidirect |
| 24. #22576080 | C22 | semidirect |
| 53. C2×D4×C271 | D4 | semidirect |
| 119. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 129. C271 | #3036 | semidirect |
| 133. C2×C4×D4 | D271 | semidirect |
| 174. C2×D4 | D1084 | semidirect |
| 250. C4 | #22576186 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576186 | 2 |
| #31774447 | 2 |
| #31774112 | 2 |
| #31774102 | 2 |
| #31774092 | 2 |
| #31773921 | 2 |
| #31773896 | 2 |
| C2×C4×D4×C271 | 2 |
| #3036 | 271 |