Finite Group DatabasebetaFinite Group DatabasebetaOrder 14528.
240 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 240 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 | #123×C227 | C2 |
| hypercenter | #123 | D227 |
| hypocenter | C227 | #540 |
| LCS | G ▷ C22×C227 ▷ C227 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20300284 | C2 | semidirect |
| 2. #20300278 | C2 | semidirect |
| 3. #20300273 | C2 | semidirect |
| 4. #20300272 | C2 | semidirect |
| 5. #20300270 | C2 | semidirect |
| 6. #20300263 | C2 | semidirect |
| 7. #20300262 | C2 | semidirect |
| 8. #20300261 | C2 | semidirect |
| 9. #20300261 | C2 | semidirect |
| 10. #20300261 | C2 | semidirect |
| 11. #20300260 | C2 | semidirect |
| 12. C4×C22⋊D227 | C2 | semidirect |
| 13. (C22⋊D227)⋊C4 | C2 | semidirect |
| 14. #20300246 | C2 | semidirect |
| 15. #123×C227 | C2 | semidirect |
| 115. C227 | #540 | semidirect |
| 122. #123 | D227 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20300284 | 2 |
| #20300278 | 2 |
| #20300273 | 2 |
| #20300272 | 2 |
| #20300270 | 2 |
| #20300263 | 2 |
| #20300262 | 2 |
| #20300261 | 2 |
| #20300260 | 2 |
| C4×C22⋊D227 | 2 |
| (C22⋊D227)⋊C4 | 2 |
| #20300246 | 2 |
| #123×C227 | 2 |
| #540 | 227 |