Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
250 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 93 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D227 |
| commutator, socle, cosocle | C22×C227 | C24 |
| Fitting | #121×C227 | C2 |
| hypercenter | #121 | D227 |
| hypocenter | C227 | #538 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20300283 | C2 | semidirect |
| 2. #20300281 | C2 | semidirect |
| 3. #20300275 | C2 | semidirect |
| 4. #20300274 | C2 | semidirect |
| 5. #20300271 | C2 | semidirect |
| 6. #20300269 | C2 | semidirect |
| 7. #20300266 | C2 | semidirect |
| 8. #20300260 | C2 | semidirect |
| 9. #20300259 | C2 | semidirect |
| 10. #20300256 | C2 | semidirect |
| 11. #20300256 | C2 | semidirect |
| 12. C4×C22⋊D227 | C2 | semidirect |
| 13. (C22⋊D227)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D227 | C2 | semidirect |
| 15. #121×C227 | C2 | semidirect |
| 17. C2×Dic454 | C22 | semidirect |
| 22. C22×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 |
| 33. C22⋊Dic227 | C22 | semidirect |
| 34. C22⋊Dic227 | C22 | semidirect |
| 35. C22⋊Dic227 | C22 | semidirect |
| 42. C4×Dic227 | C22 | semidirect |
| 43. C4×Dic227 | C22 | semidirect |
| 46. C2×D4×C227 | C22 | semidirect |
| 47. C22×C4×C227 | C22 | semidirect |
| 48. C4⋊C4×C227 | C22 | semidirect |
| 50. C22⋊C4×C227 | C22 | semidirect |
| 116. C227 | #538 | semidirect |
| 127. #121 | D227 | semidirect |
| 141. C2×D4 | C2×D227 | semidirect |
| 145. C22×C4 | C2×D227 | semidirect |
| 151. C4⋊C4 | C2×D227 | semidirect |
| 165. C22⋊C4 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300283 | 2 |
| #20300281 | 2 |
| #20300275 | 2 |
| #20300274 | 2 |
| #20300271 | 2 |
| #20300269 | 2 |
| #20300266 | 2 |
| #20300260 | 2 |
| #20300259 | 2 |
| #20300256 | 2 |
| C4×C22⋊D227 | 2 |
| (C22⋊D227)⋊C4 | 2 |
| C22⋊C4×D227 | 2 |
| #121×C227 | 2 |
| #538 | 227 |