Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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 | #126×C227 | C2 |
| prime radical | C2×C22⋊D227 | C22 |
| hypercenter | #126 | D227 |
| hypocenter | C227 | #563 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20300288 | C2 | semidirect |
| 2. #20300287 | C2 | semidirect |
| 3. #20300283 | C2 | semidirect |
| 4. #20300282 | C2 | semidirect |
| 5. #20300281 | C2 | semidirect |
| 6. #20300279 | C2 | semidirect |
| 7. #20300278 | C2 | semidirect |
| 11. #20300268 | C2 | semidirect |
| 12. #20300266 | C2 | semidirect |
| 13. #20300265 | C2 | semidirect |
| 14. #20300265 | C2 | semidirect |
| 15. #126×C227 | C2 | semidirect |
| 97. C227 | #563 | semidirect |
| 104. #126 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300288 | 2 |
| #20300287 | 2 |
| #20300283 | 2 |
| #20300282 | 2 |
| #20300281 | 2 |
| #20300279 | 2 |
| #20300278 | 2 |
| #20300274 | 2 |
| #20300272 | 2 |
| #20300270 | 2 |
| #20300268 | 2 |
| #20300266 | 2 |
| #20300265 | 2 |
| #126×C227 | 2 |
| #563 | 227 |