Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
196 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 196 conjugacy classes of subgroups — too many to draw. Only its 91 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×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Fitting | #126×C43 | C2 |
| prime radical | C2×C22⋊D43 | C22 |
| hypercenter | #126 | D43 |
| hypocenter | C43 | #563 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #126 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063325 | C2 | semidirect |
| 2. #13063324 | C2 | semidirect |
| 3. #13063320 | C2 | semidirect |
| 4. #13063319 | C2 | semidirect |
| 5. #13063318 | C2 | semidirect |
| 6. #13063316 | C2 | semidirect |
| 7. #13063315 | C2 | semidirect |
| 11. #13063305 | C2 | semidirect |
| 12. #13063303 | C2 | semidirect |
| 13. #13063302 | C2 | semidirect |
| 14. #13063302 | C2 | semidirect |
| 15. #126×C43 | C2 | semidirect |
| 98. C43 | #563 | semidirect |
| 104. #126 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063325 | 2 |
| #13063324 | 2 |
| #13063320 | 2 |
| #13063319 | 2 |
| #13063318 | 2 |
| #13063316 | 2 |
| #13063315 | 2 |
| #13063311 | 2 |
| #13063309 | 2 |
| #13063307 | 2 |
| #13063305 | 2 |
| #13063303 | 2 |
| #13063302 | 2 |
| #126×C43 | 2 |
| #563 | 43 |