Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
214 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 214 conjugacy classes of subgroups — too many to draw. Only its 97 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×D223 |
| commutator, socle, cosocle | C22×C223 | C24 |
| Fitting | #123×C223 | C2 |
| prime radical | C2×D4×C223 | C22 |
| hypercenter | #123 | D223 |
| hypocenter | C223 | #552 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20297297 | C2 | semidirect |
| 2. #20297297 | C2 | semidirect |
| 3. #20297295 | C2 | semidirect |
| 4. #20297294 | C2 | semidirect |
| 5. #20297294 | C2 | semidirect |
| 7. #20297281 | C2 | semidirect |
| 8. #20297281 | C2 | semidirect |
| 9. #20297269 | C2 | semidirect |
| 11. #20297263 | C2 | semidirect |
| 12. #20297260 | C2 | semidirect |
| 13. #20297260 | C2 | semidirect |
| 14. C2×Dic223⋊C4 | C2 | semidirect |
| 97. C223 | #552 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297297 | 2 |
| #20297295 | 2 |
| #20297294 | 2 |
| #20297285 | 2 |
| #20297281 | 2 |
| #20297269 | 2 |
| D4×Dic223 | 2 |
| #20297263 | 2 |
| #20297260 | 2 |
| C2×Dic223⋊C4 | 2 |
| #123×C223 | 2 |
| #552 | 223 |