Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
234 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 234 conjugacy classes of subgroups — too many to draw. Only its 99 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 | #123×C43 | C2 |
| prime radical | #13063297 | C2 |
| hypercenter | #123 | D43 |
| hypocenter | C43 | #529 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #123 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063320 | C2 | semidirect |
| 2. #13063318 | C2 | semidirect |
| 3. #13063315 | C2 | semidirect |
| 4. #13063311 | C2 | semidirect |
| 5. #13063308 | C2 | semidirect |
| 6. #13063302 | C2 | semidirect |
| 8. #13063290 | C2 | semidirect |
| 9. D4×Dic43 | C2 | semidirect |
| 10. (C22⋊D43)⋊C4 | C2 | semidirect |
| 11. (C22⋊D43)⋊C4 | C2 | semidirect |
| 12. #13063283 | C2 | semidirect |
| 13. #13063281 | C2 | semidirect |
| 14. C2×C4×Dic43 | C2 | semidirect |
| 15. #123×C43 | C2 | semidirect |
| 104. C43 | #529 | semidirect |
| 110. #123 | D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063320 | 2 |
| #13063318 | 2 |
| #13063315 | 2 |
| #13063311 | 2 |
| #13063308 | 2 |
| #13063302 | 2 |
| #13063297 | 2 |
| #13063290 | 2 |
| D4×Dic43 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| #13063283 | 2 |
| #13063281 | 2 |
| C2×C4×Dic43 | 2 |
| #123×C43 | 2 |
| #529 | 43 |