Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
240 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 240 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 | #121×C227 | C2 |
| hypercenter | #121 | D227 |
| hypocenter | C227 | #540 |
| 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. #20300284 | C2 | semidirect |
| 2. #20300279 | C2 | semidirect |
| 3. #20300272 | C2 | semidirect |
| 4. #20300270 | C2 | semidirect |
| 5. #20300262 | C2 | semidirect |
| 6. #20300260 | C2 | semidirect |
| 7. #20300259 | C2 | semidirect |
| 8. D4×Dic227 | C2 | semidirect |
| 9. #20300250 | C2 | semidirect |
| 10. #20300247 | C2 | semidirect |
| 11. #121×C227 | C2 | semidirect |
| 79. C227 | #540 | semidirect |
| 88. #121 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300284 | 2 |
| #20300279 | 2 |
| #20300272 | 2 |
| #20300270 | 2 |
| #20300262 | 2 |
| #20300260 | 2 |
| #20300259 | 2 |
| D4×Dic227 | 2 |
| #20300250 | 2 |
| #20300247 | 2 |
| #121×C227 | 2 |
| #540 | 227 |