Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
548 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 131 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×#22576184 | C2 | semidirect |
| 2. #31774445 | C2 | semidirect |
| 3. C4×D4×D271 | C2 | semidirect |
| 4. #31774111 | C2 | semidirect |
| 5. #31774110 | C2 | semidirect |
| 6. #31774103 | C2 | semidirect |
| 7. #31774102 | C2 | semidirect |
| 8. #31774089 | C2 | semidirect |
| 9. #31773919 | C2 | semidirect |
| 10. #31773895 | C2 | semidirect |
| 11. #459×C271 | C2 | semidirect |
| 20. #22576160 | C22 | semidirect |
| 21. #22576147 | C22 | semidirect |
| 34. C4⋊(C271⋊C8) | C22 | semidirect |
| 35. Dic271⋊C8 | C22 | semidirect |
| 36. #22576085 | C22 | semidirect |
| 37. #22576083 | C22 | semidirect |
| 38. #22576081 | C22 | semidirect |
| 40. #127×C271 | C22 | semidirect |
| 42. C4⋊C8×C271 | C22 | semidirect |
| 43. #102×C271 | C22 | semidirect |
| 52. D4×D271 | D4 | semidirect |
| 145. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 160. C271 | #3036 | semidirect |
| 170. #459 | D271 | semidirect |
| 183. #127 | C2×D271 | semidirect |
| 200. C4⋊C8 | C2×D271 | semidirect |
| 204. #102 | C2×D271 | semidirect |
| 311. C4 | #22576184 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576184 | 2 |
| #31774445 | 2 |
| C4×D4×D271 | 2 |
| #31774111 | 2 |
| #31774110 | 2 |
| #31774103 | 2 |
| #31774102 | 2 |
| #31774089 | 2 |
| #31773919 | 2 |
| #31773895 | 2 |
| #459×C271 | 2 |
| #3036 | 271 |