Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
596 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 149 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. C2×#22576180 | C2 | semidirect |
| 3. C22×#16864639 | C2 | semidirect |
| 4. #31774464 | C2 | semidirect |
| 5. #31774461 | C2 | semidirect |
| 6. #31774285 | C2 | semidirect |
| 7. #31774283 | C2 | semidirect |
| 8. #31774278 | C2 | semidirect |
| 9. #31774272 | C2 | semidirect |
| 10. #31773855 | C2 | semidirect |
| 11. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 16. C2×#16864644 | C22 | semidirect |
| 17. C2×#16864643 | C22 | semidirect |
| 18. C2×#16864642 | C22 | semidirect |
| 19. C2×#16864641 | C22 | semidirect |
| 20. C2×D2168 | C22 | semidirect |
| 24. C2×#16864639 | C22 | semidirect |
| 26. #22576156 | C22 | semidirect |
| 27. #22576156 | C22 | semidirect |
| 28. #22576149 | C22 | semidirect |
| 29. #22576147 | C22 | semidirect |
| 35. #22576070 | C22 | semidirect |
| 36. C8×Dic271 | C22 | semidirect |
| 40. C2×SD16×C271 | C22 | semidirect |
| 41. C2×D8×C271 | C22 | semidirect |
| 64. C2×C271⋊C8 | D4 | semidirect |
| 86. M16×C271 | D4 | semidirect |
| 153. C271 | #3155 | semidirect |
| 156. C2×AGL(1,ℤ/8) | D271 | semidirect |
| 177. C2×SD16 | C2×D271 | semidirect |
| 183. C2×D8 | C2×D271 | semidirect |
| 232. M16 | C22⋊D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576188 | 2 |
| C2×#22576180 | 2 |
| C22×#16864639 | 2 |
| #31774464 | 2 |
| #31774461 | 2 |
| #31774285 | 2 |
| #31774283 | 2 |
| #31774278 | 2 |
| #31774272 | 2 |
| #31773855 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3155 | 271 |