Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
462 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 462 conjugacy classes of subgroups — too many to draw. Only its 121 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×#22576118 | C2 | semidirect |
| 3. #31774224 | C2 | semidirect |
| 4. #31774220 | C2 | semidirect |
| 5. #31774216 | C2 | semidirect |
| 6. #31774213 | C2 | semidirect |
| 7. #31774210 | C2 | semidirect |
| 8. #31773938 | C2 | semidirect |
| 9. #31773900 | C2 | semidirect |
| 10. #31773859 | C2 | semidirect |
| 11. #480×C271 | C2 | semidirect |
| 24. #22576118 | C22 | semidirect |
| 25. C2×C4⋊Dic271 | C22 | semidirect |
| 30. #22576093 | C22 | semidirect |
| 31. #22576092 | C22 | semidirect |
| 32. #22576091 | C22 | semidirect |
| 33. #22576082 | C22 | semidirect |
| 34. #22576081 | C22 | semidirect |
| 35. #22576080 | C22 | semidirect |
| 36. C22⋊(C271⋊C8) | C22 | semidirect |
| 37. (C2×D271)⋊C8 | C22 | semidirect |
| 39. C2×C4⋊C4×C271 | C22 | semidirect |
| 40. #107×C271 | C22 | semidirect |
| 41. #102×C271 | C22 | semidirect |
| 42. C22⋊C8×C271 | C22 | semidirect |
| 153. C271 | #3094 | semidirect |
| 162. #480 | D271 | semidirect |
| 182. C2×C4⋊C4 | C2×D271 | semidirect |
| 187. #107 | C2×D271 | semidirect |
| 193. #102 | C2×D271 | semidirect |
| 196. C22⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #121×D271 | 2 |
| C2×#22576118 | 2 |
| #31774224 | 2 |
| #31774220 | 2 |
| #31774216 | 2 |
| #31774213 | 2 |
| #31774210 | 2 |
| #31773938 | 2 |
| #31773900 | 2 |
| #31773859 | 2 |
| #480×C271 | 2 |
| #3094 | 271 |