Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
248 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 248 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×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Fitting | #123×C43 | C2 |
| prime radical | #13063293 | C2 |
| hypercenter | #123 | D43 |
| hypocenter | C43 | #551 |
| 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. #13063318 | C2 | semidirect |
| 2. #13063312 | C2 | semidirect |
| 3. #13063307 | C2 | semidirect |
| 4. #13063303 | C2 | semidirect |
| 6. C4×C22⋊D43 | C2 | semidirect |
| 7. #13063283 | C2 | semidirect |
| 8. C22⋊C4×D43 | C2 | semidirect |
| 9. #123×C43 | C2 | semidirect |
| 12. C22×C4×C43 | C22 | semidirect |
| 16. C2×Dic86 | C22 | semidirect |
| 17. C4⋊C4×C43 | C22 | semidirect |
| 19. C22⋊C4×C43 | C22 | semidirect |
| 22. C22⋊Dic43 | C22 | semidirect |
| 26. C4⋊Dic43 | C22 | semidirect |
| 27. Dic43⋊C4 | C22 | semidirect |
| 28. Dic43⋊C4 | C22 | semidirect |
| 29. C4×Dic43 | C22 | semidirect |
| 30. C4×Dic43 | C22 | semidirect |
| 69. C43 | #551 | semidirect |
| 73. #123 | D43 | semidirect |
| 85. C22×C4 | C2×D43 | semidirect |
| 89. C4⋊C4 | C2×D43 | semidirect |
| 97. C22⋊C4 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063318 | 2 |
| #13063312 | 2 |
| #13063307 | 2 |
| #13063303 | 2 |
| #13063293 | 2 |
| C4×C22⋊D43 | 2 |
| #13063283 | 2 |
| C22⋊C4×D43 | 2 |
| #123×C43 | 2 |
| #551 | 43 |