Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
330 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
| hypercenter | #123 | D43 |
| hypocenter | C43 | #525 |
| 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. C2×#10621900 | C2 | semidirect |
| 2. C22×C4×D43 | C2 | semidirect |
| 3. #13063308 | C2 | semidirect |
| 4. #13063303 | C2 | semidirect |
| 5. #13063298 | C2 | semidirect |
| 6. #13063295 | C2 | semidirect |
| 7. #13063293 | C2 | semidirect |
| 8. #13063287 | C2 | semidirect |
| 9. (C22⋊D43)⋊C4 | C2 | semidirect |
| 10. #13063281 | C2 | semidirect |
| 11. #123×C43 | C2 | semidirect |
| 17. C2×C22⋊D43 | C22 | semidirect |
| 19. C22×Dic43 | C22 | semidirect |
| 25. C2×C4×D43 | C22 | semidirect |
| 26. C2×Dic86 | C22 | semidirect |
| 27. C4⋊C4×C43 | C22 | semidirect |
| 29. C22⋊C4×C43 | C22 | semidirect |
| 33. (C2×D43)⋊C4 | C22 | semidirect |
| 34. Dic43⋊C4 | C22 | semidirect |
| 35. Dic43⋊C4 | C22 | semidirect |
| 36. C4×Dic43 | C22 | semidirect |
| 52. C2×Dic43 | D4 | semidirect |
| 72. C2×D43 | #41 | semidirect |
| 87. C43 | #525 | semidirect |
| 91. #123 | D43 | semidirect |
| 116. C4⋊C4 | C2×D43 | semidirect |
| 122. C22⋊C4 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621900 | 2 |
| C22×C4×D43 | 2 |
| #13063308 | 2 |
| #13063303 | 2 |
| #13063298 | 2 |
| #13063295 | 2 |
| #13063293 | 2 |
| #13063287 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| #13063281 | 2 |
| #123×C43 | 2 |
| #525 | 43 |