Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
440 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 440 conjugacy classes of subgroups — too many to draw. Only its 153 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. #31774454 | C2 | semidirect |
| 2. #31774197 | C2 | semidirect |
| 3. #31774187 | C2 | semidirect |
| 4. #31774177 | C2 | semidirect |
| 5. #31773937 | C2 | semidirect |
| 6. #31773921 | C2 | semidirect |
| 10. #22576160 | C22 | semidirect |
| 11. #22576160 | C22 | semidirect |
| 12. #22576152 | C22 | semidirect |
| 18. #22576093 | C22 | semidirect |
| 19. #22576091 | C22 | semidirect |
| 20. C4⋊(C271⋊C8) | C22 | semidirect |
| 21. C4⋊(C271⋊C8) | C22 | semidirect |
| 48. C2×D4×C271 | Q8 | semidirect |
| 115. C271 | #3077 | semidirect |
| 154. C2×D4 | Dic542 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #31774454 | 2 |
| #31774197 | 2 |
| #31774187 | 2 |
| #31774177 | 2 |
| #31773937 | 2 |
| #31773921 | 2 |
| #31773902 | 2 |
| C2×C4×D4×C271 | 2 |
| #3077 | 271 |