Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
250 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 250 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 | #121×C43 | C2 |
| hypercenter | #121 | D43 |
| hypocenter | C43 | #538 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #121 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063320 | C2 | semidirect |
| 2. #13063311 | C2 | semidirect |
| 3. #13063309 | C2 | semidirect |
| 4. #13063304 | C2 | semidirect |
| 5. #13063297 | C2 | semidirect |
| 6. #13063293 | C2 | semidirect |
| 7. D4×Dic43 | C2 | semidirect |
| 8. C2×(C2×D43)⋊C4 | C2 | semidirect |
| 9. #121×C43 | C2 | semidirect |
| 12. C2×D4×C43 | C22 | semidirect |
| 17. C22×Dic43 | C22 | semidirect |
| 18. C2×Dic86 | C22 | semidirect |
| 19. C4⋊C4×C43 | C22 | semidirect |
| 20. C22⋊C4×C43 | C22 | semidirect |
| 22. C22⋊Dic43 | C22 | semidirect |
| 27. C4⋊Dic43 | C22 | semidirect |
| 28. C4⋊Dic43 | C22 | semidirect |
| 29. Dic43⋊C4 | C22 | semidirect |
| 30. C4×Dic43 | C22 | semidirect |
| 75. C43 | #538 | semidirect |
| 81. #121 | D43 | semidirect |
| 90. C2×D4 | C2×D43 | semidirect |
| 97. C4⋊C4 | C2×D43 | semidirect |
| 104. C22⋊C4 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063320 | 2 |
| #13063311 | 2 |
| #13063309 | 2 |
| #13063304 | 2 |
| #13063297 | 2 |
| #13063293 | 2 |
| D4×Dic43 | 2 |
| C2×(C2×D43)⋊C4 | 2 |
| #121×C43 | 2 |
| #538 | 43 |