Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
330 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D43 |
| commutator, socle, cosocle | C22×C43 | C24 |
| Frattini | C22 | C23×D43 |
| Fitting | C4×D4×C43 | C2 |
| hypercenter | C4×D4 | D43 |
| hypocenter | C43 | #525 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C4×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#10621898 | C2 | semidirect |
| 2. C22×C4×D43 | C2 | semidirect |
| 3. #13063310 | C2 | semidirect |
| 4. #13063307 | C2 | semidirect |
| 5. #13063303 | C2 | semidirect |
| 6. #13063302 | C2 | semidirect |
| 7. #13063298 | C2 | semidirect |
| 8. #13063297 | C2 | semidirect |
| 9. #13063295 | C2 | semidirect |
| 10. #13063293 | C2 | semidirect |
| 11. C4×D172 | C2 | semidirect |
| 12. C4×C22⋊D43 | C2 | semidirect |
| 13. C4×C22⋊D43 | C2 | semidirect |
| 14. #13063282 | C2 | semidirect |
| 15. C4×D4×C43 | C2 | semidirect |
| 19. C22×C4×C43 | C22 | semidirect |
| 23. C2×C22⋊D43 | C22 | semidirect |
| 33. C2×C4×D43 | C22 | semidirect |
| 34. C2×Dic86 | C22 | semidirect |
| 35. C4⋊C4×C43 | C22 | semidirect |
| 37. C22⋊C4×C43 | C22 | semidirect |
| 38. C42×C43 | C22 | semidirect |
| 40. C22⋊Dic43 | C22 | semidirect |
| 45. (C2×D43)⋊C4 | C22 | semidirect |
| 46. (C2×D43)⋊C4 | C22 | semidirect |
| 47. C4⋊Dic43 | C22 | semidirect |
| 48. Dic43⋊C4 | C22 | semidirect |
| 49. Dic43⋊C4 | C22 | semidirect |
| 50. Dic43⋊C4 | C22 | semidirect |
| 51. Dic43⋊C4 | C22 | semidirect |
| 52. C4×Dic43 | C22 | semidirect |
| 85. C4×D43 | D4 | semidirect |
| 92. C22×C43 | #41 | semidirect |
| 103. C2×D43 | #41 | semidirect |
| 123. C43 | #525 | semidirect |
| 137. C4×D4 | D43 | semidirect |
| 157. C22×C4 | C2×D43 | semidirect |
| 163. C4⋊C4 | C2×D43 | semidirect |
| 173. C22⋊C4 | C2×D43 | semidirect |
| 175. C42 | C2×D43 | semidirect |
| 225. C22 | #10621898 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10621898 | 2 |
| C22×C4×D43 | 2 |
| #13063310 | 2 |
| #13063307 | 2 |
| #13063303 | 2 |
| #13063302 | 2 |
| #13063298 | 2 |
| #13063297 | 2 |
| #13063295 | 2 |
| #13063293 | 2 |
| C4×D172 | 2 |
| C4×C22⋊D43 | 2 |
| #13063282 | 2 |
| C4×D4×C43 | 2 |
| #525 | 43 |