Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
548 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 145 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×#22576188 | C2 | semidirect |
| 2. #31774447 | C2 | semidirect |
| 3. C2×C4×D1084 | C2 | semidirect |
| 4. #31774113 | C2 | semidirect |
| 5. #31774103 | C2 | semidirect |
| 6. #31774093 | C2 | semidirect |
| 7. #31773899 | C2 | semidirect |
| 8. #423×C271 | C2 | semidirect |
| 15. #22576160 | C22 | semidirect |
| 16. #22576157 | C22 | semidirect |
| 17. #22576148 | C22 | semidirect |
| 28. #22576085 | C22 | semidirect |
| 29. #22576082 | C22 | semidirect |
| 32. C4⋊C8×C271 | C22 | semidirect |
| 33. C4⋊C8×C271 | C22 | semidirect |
| 42. C2×D1084 | D4 | semidirect |
| 118. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 129. C271 | #3036 | semidirect |
| 137. #423 | D271 | semidirect |
| 160. C4⋊C8 | C2×D271 | semidirect |
| 161. C4⋊C8 | C2×D271 | semidirect |
| 250. C4 | #22576188 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| #31774447 | 2 |
| C2×C4×D1084 | 2 |
| #31774113 | 2 |
| #31774103 | 2 |
| #31774093 | 2 |
| #31773899 | 2 |
| #423×C271 | 2 |
| #3036 | 271 |