Finite Group DatabasebetaFinite Group DatabasebetaOrder 34688.
1116 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1116 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 |
|---|---|---|
| 2. C2×#22576143 | C2 | semidirect |
| 3. #31773812 | C2 | semidirect |
| 4. #31773776 | C2 | semidirect |
| 5. #31773769 | C2 | semidirect |
| 6. #31773753 | C2 | semidirect |
| 7. #31773752 | C2 | semidirect |
| 8. C22×C22⋊C4×C271 | C2 | semidirect |
| 16. C2×Dic271⋊C4 | C22 | semidirect |
| 18. C2×C22⋊Dic271 | C22 | semidirect |
| 19. C2×C22⋊Dic271 | C22 | semidirect |
| 20. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 21. C2×(C2×D271)⋊C4 | C22 | semidirect |
| 22. C271⋊#95 | C22 | semidirect |
| 24. C23×C4×C271 | C22 | semidirect |
| 25. C23×C4×C271 | C22 | semidirect |
| 28. C2×C22⋊C4×C271 | C22 | semidirect |
| 119. C22×C271 | #123 | semidirect |
| 142. C271 | #2405 | semidirect |
| 146. C22×C22⋊C4 | D271 | semidirect |
| 159. C23×C4 | C2×D271 | semidirect |
| 160. C23×C4 | C2×D271 | semidirect |
| 170. C2×C22⋊C4 | C2×D271 | semidirect |
| 268. C22 | #22576143 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C22⋊D271 | 2 |
| C2×#22576143 | 2 |
| #31773812 | 2 |
| #31773776 | 2 |
| #31773769 | 2 |
| #31773753 | 2 |
| #31773752 | 2 |
| C22×C22⋊C4×C271 | 2 |
| #2405 | 271 |