Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 95 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 | #124×C227 | C2 |
| prime radical | #20300256 | C2 |
| hypercenter | #124 | D227 |
| hypocenter | C227 | #551 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20300281 | C2 | semidirect |
| 2. #20300270 | C2 | semidirect |
| 3. #20300269 | C2 | semidirect |
| 4. #20300264 | C2 | semidirect |
| 6. (C22⋊D227)⋊C4 | C2 | semidirect |
| 7. #20300245 | C2 | semidirect |
| 8. C22⋊C4×D227 | C2 | semidirect |
| 9. #124×C227 | C2 | semidirect |
| 12. C22×Dic227 | C22 | semidirect |
| 15. C4⋊Dic227 | C22 | semidirect |
| 16. Dic227⋊C4 | C22 | semidirect |
| 17. Dic227⋊C4 | C22 | semidirect |
| 18. Dic227⋊C4 | C22 | semidirect |
| 21. C22⋊Dic227 | C22 | semidirect |
| 25. C4×Dic227 | C22 | semidirect |
| 26. C2×Q8×C227 | C22 | semidirect |
| 29. C22⋊C4×C227 | C22 | semidirect |
| 30. C42×C227 | C22 | semidirect |
| 68. C227 | #551 | semidirect |
| 71. #124 | D227 | semidirect |
| 80. C2×Q8 | C2×D227 | semidirect |
| 97. C22⋊C4 | C2×D227 | semidirect |
| 99. C42 | C2×D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300281 | 2 |
| #20300270 | 2 |
| #20300269 | 2 |
| #20300264 | 2 |
| #20300256 | 2 |
| (C22⋊D227)⋊C4 | 2 |
| #20300245 | 2 |
| C22⋊C4×D227 | 2 |
| #124×C227 | 2 |
| #551 | 227 |