Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
656 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 157 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. #31774284 | C2 | semidirect |
| 4. #31774273 | C2 | semidirect |
| 5. #31774269 | C2 | semidirect |
| 6. C4×#16864638 | C2 | semidirect |
| 7. C2×#127×C271 | C2 | semidirect |
| 10. C2×#16864642 | C22 | semidirect |
| 11. C2×#16864639 | C22 | semidirect |
| 13. #22576160 | C22 | semidirect |
| 14. #22576157 | C22 | semidirect |
| 15. #22576148 | C22 | semidirect |
| 18. #22576071 | C22 | semidirect |
| 19. C4×C271⋊C8 | C22 | semidirect |
| 34. #16864638 | D4 | semidirect |
| 57. C271⋊C8 | C2×D4 | semidirect |
| 82. C4×C271 | AGL(1,ℤ/8) | semidirect |
| 90. C271 | #3151 | semidirect |
| 94. C2×#127 | D271 | semidirect |
| 174. 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 |
| #31774284 | 2 |
| #31774273 | 2 |
| #31774269 | 2 |
| C4×#16864638 | 2 |
| C2×#127×C271 | 2 |
| #3151 | 271 |