Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
248 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 99 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. #20300281 | C2 | semidirect |
| 2. #20300281 | C2 | semidirect |
| 3. #20300274 | C2 | semidirect |
| 4. #20300272 | C2 | semidirect |
| 5. #20300271 | C2 | semidirect |
| 6. #20300270 | C2 | semidirect |
| 7. #20300267 | C2 | semidirect |
| 8. #20300265 | C2 | semidirect |
| 10. C4×C22⋊D227 | C2 | semidirect |
| 11. (C22⋊D227)⋊C4 | C2 | semidirect |
| 12. #20300247 | C2 | semidirect |
| 13. #20300244 | C2 | semidirect |
| 14. C2×C22⋊Dic227 | C2 | semidirect |
| 15. C2×C22⋊C4×C227 | C2 | semidirect |
| 16. C2×Dic454 | C22 | semidirect |
| 22. C2×C4×D227 | C22 | semidirect |
| 23. C4⋊Dic227 | C22 | semidirect |
| 24. C4⋊Dic227 | C22 | semidirect |
| 25. C4⋊Dic227 | C22 | semidirect |
| 26. Dic227⋊C4 | C22 | semidirect |
| 27. Dic227⋊C4 | C22 | semidirect |
| 28. Dic227⋊C4 | C22 | semidirect |
| 29. Dic227⋊C4 | C22 | semidirect |
| 30. Dic227⋊C4 | C22 | semidirect |
| 38. (C2×D227)⋊C4 | C22 | semidirect |
| 39. (C2×D227)⋊C4 | C22 | semidirect |
| 40. (C2×D227)⋊C4 | C22 | semidirect |
| 41. C4×Dic227 | C22 | semidirect |
| 42. C4×Dic227 | C22 | semidirect |
| 43. C4×Dic227 | C22 | semidirect |
| 110. C227 | #551 | semidirect |
| 126. C2×C22⋊C4 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300281 | 2 |
| #20300274 | 2 |
| #20300272 | 2 |
| #20300271 | 2 |
| #20300270 | 2 |
| #20300267 | 2 |
| #20300265 | 2 |
| #20300257 | 2 |
| C4×C22⋊D227 | 2 |
| (C22⋊D227)⋊C4 | 2 |
| #20300247 | 2 |
| #20300244 | 2 |
| C2×C22⋊Dic227 | 2 |
| C2×C22⋊C4×C227 | 2 |
| #551 | 227 |