Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
492 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 181 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×#22576168 | C2 | semidirect |
| 2. C22×#16864637 | C2 | semidirect |
| 4. #31773974 | C2 | semidirect |
| 5. #31773967 | C2 | semidirect |
| 6. #31773863 | C2 | semidirect |
| 7. #31773860 | C2 | semidirect |
| 8. #31773853 | C2 | semidirect |
| 9. #424×C271 | C2 | semidirect |
| 17. C2×#16864637 | C22 | semidirect |
| 19. C2×C8×D271 | C22 | semidirect |
| 26. (C2×D271)⋊C8 | C22 | semidirect |
| 27. #22576071 | C22 | semidirect |
| 28. C4×C271⋊C8 | C22 | semidirect |
| 32. C4⋊C8×C271 | C22 | semidirect |
| 50. C2×C271⋊C8 | D4 | semidirect |
| 113. C271 | #2930 | semidirect |
| 120. #424 | D271 | semidirect |
| 142. C4⋊C8 | C2×D271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22576168 | 2 |
| C22×#16864637 | 2 |
| #31774409 | 2 |
| #31773974 | 2 |
| #31773967 | 2 |
| #31773863 | 2 |
| #31773860 | 2 |
| #31773853 | 2 |
| #424×C271 | 2 |
| #2930 | 271 |