Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
466 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 137 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. #31774695 | C2 | semidirect |
| 2. C2×#22576186 | C2 | semidirect |
| 3. #31774664 | C2 | semidirect |
| 4. #31774165 | C2 | semidirect |
| 5. #31774158 | C2 | semidirect |
| 6. #31773945 | C2 | semidirect |
| 7. #31773879 | C2 | semidirect |
| 8. C2×#22576077 | C2 | semidirect |
| 9. C2×AGL(1,ℤ/8)×C271 | C2 | semidirect |
| 12. #22576190 | C22 | semidirect |
| 16. #22576185 | C22 | semidirect |
| 18. C2×#16864642 | C22 | semidirect |
| 19. C2×#16864639 | C22 | semidirect |
| 21. #22576167 | C22 | semidirect |
| 26. #22576095 | C22 | semidirect |
| 27. #22576078 | C22 | semidirect |
| 28. #22576077 | C22 | semidirect |
| 29. #22576076 | C22 | semidirect |
| 147. C271 | #3068 | semidirect |
| 151. C2×AGL(1,ℤ/8) | D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774695 | 2 |
| C2×#22576186 | 2 |
| #31774664 | 2 |
| #31774165 | 2 |
| #31774158 | 2 |
| #31773945 | 2 |
| #31773879 | 2 |
| C2×#22576077 | 2 |
| C2×AGL(1,ℤ/8)×C271 | 2 |
| #3068 | 271 |