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 | C4×D4×C227 | C2 |
| hypercenter | C4×D4 | D227 |
| hypocenter | C227 | #540 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20300284 | C2 | semidirect |
| 2. #20300279 | C2 | semidirect |
| 3. #20300271 | C2 | semidirect |
| 4. #20300270 | C2 | semidirect |
| 5. #20300263 | C2 | semidirect |
| 6. #20300262 | C2 | semidirect |
| 7. #20300261 | C2 | semidirect |
| 8. #20300259 | C2 | semidirect |
| 9. C4×D908 | C2 | semidirect |
| 10. #20300245 | C2 | semidirect |
| 11. C4×D4×C227 | C2 | semidirect |
| 79. C227 | #540 | semidirect |
| 90. C4×D4 | 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 |
| #20300271 | 2 |
| #20300270 | 2 |
| #20300263 | 2 |
| #20300262 | 2 |
| #20300261 | 2 |
| #20300259 | 2 |
| C4×D908 | 2 |
| #20300245 | 2 |
| C4×D4×C227 | 2 |
| #540 | 227 |