Finite Group DatabasebetaFinite Group DatabasebetaOrder 14272.
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×D223 |
| commutator, socle, cosocle | C22×C223 | C24 |
| Fitting | #121×C223 | C2 |
| hypercenter | #121 | D223 |
| hypocenter | C223 | #540 |
| LCS | G ▷ C22×C223 ▷ C223 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #20297300 | C2 | semidirect |
| 2. #20297295 | C2 | semidirect |
| 3. #20297288 | C2 | semidirect |
| 4. #20297286 | C2 | semidirect |
| 5. #20297278 | C2 | semidirect |
| 6. #20297276 | C2 | semidirect |
| 7. #20297275 | C2 | semidirect |
| 8. D4×Dic223 | C2 | semidirect |
| 9. #20297266 | C2 | semidirect |
| 10. #20297263 | C2 | semidirect |
| 11. #121×C223 | C2 | semidirect |
| 79. C223 | #540 | semidirect |
| 88. #121 | D223 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #20297300 | 2 |
| #20297295 | 2 |
| #20297288 | 2 |
| #20297286 | 2 |
| #20297278 | 2 |
| #20297276 | 2 |
| #20297275 | 2 |
| D4×Dic223 | 2 |
| #20297266 | 2 |
| #20297263 | 2 |
| #121×C223 | 2 |
| #540 | 223 |