Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
236 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 236 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 | #124×C223 | C2 |
| prime radical | #20297300 | C2 |
| hypercenter | #124 | D223 |
| hypocenter | C223 | #559 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ #124 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #20297293 | C2 | semidirect |
| 3. #20297290 | C2 | semidirect |
| 4. #20297288 | C2 | semidirect |
| 5. #20297286 | C2 | semidirect |
| 6. Q8×Dic223 | C2 | semidirect |
| 7. C4×Dic446 | C2 | semidirect |
| 8. C4×D892 | C2 | semidirect |
| 9. D4×Dic223 | C2 | semidirect |
| 10. (C22⋊D223)⋊C4 | C2 | semidirect |
| 11. #124×C223 | C2 | semidirect |
| 75. C223 | #559 | semidirect |
| 80. #124 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297300 | 2 |
| #20297293 | 2 |
| #20297290 | 2 |
| #20297288 | 2 |
| #20297286 | 2 |
| Q8×Dic223 | 2 |
| C4×Dic446 | 2 |
| C4×D892 | 2 |
| D4×Dic223 | 2 |
| (C22⋊D223)⋊C4 | 2 |
| #124×C223 | 2 |
| #559 | 223 |