Finite Group DatabasebetaFinite Group DatabasebetaOrder 2752.
248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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 | #117×C43 | C2 |
| prime radical | #13063295 | C2 |
| hypercenter | #117 | D43 |
| hypocenter | C43 | #551 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ #117 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13063320 | C2 | semidirect |
| 2. #13063319 | C2 | semidirect |
| 3. #13063313 | C2 | semidirect |
| 4. #13063310 | C2 | semidirect |
| 5. #13063310 | C2 | semidirect |
| 6. #13063308 | C2 | semidirect |
| 7. #13063303 | C2 | semidirect |
| 8. #13063302 | C2 | semidirect |
| 10. C4×D172 | C2 | semidirect |
| 11. (C22⋊D43)⋊C4 | C2 | semidirect |
| 12. #13063282 | C2 | semidirect |
| 13. C2×(C2×D43)⋊C4 | C2 | semidirect |
| 14. C22⋊C4×D43 | C2 | semidirect |
| 15. #117×C43 | C2 | semidirect |
| 24. C2×C4×D43 | C22 | semidirect |
| 25. C2×Dic86 | C22 | semidirect |
| 26. C4⋊C4×C43 | C22 | semidirect |
| 27. C4⋊C4×C43 | C22 | semidirect |
| 30. C42×C43 | C22 | semidirect |
| 31. C42×C43 | C22 | semidirect |
| 41. (C2×D43)⋊C4 | C22 | semidirect |
| 42. (C2×D43)⋊C4 | C22 | semidirect |
| 43. (C2×D43)⋊C4 | C22 | semidirect |
| 44. C4⋊Dic43 | C22 | semidirect |
| 45. Dic43⋊C4 | C22 | semidirect |
| 46. Dic43⋊C4 | C22 | semidirect |
| 47. Dic43⋊C4 | C22 | semidirect |
| 48. Dic43⋊C4 | C22 | semidirect |
| 49. Dic43⋊C4 | C22 | semidirect |
| 50. C4×Dic43 | C22 | semidirect |
| 111. C43 | #551 | semidirect |
| 124. #117 | D43 | semidirect |
| 143. C4⋊C4 | C2×D43 | semidirect |
| 144. C4⋊C4 | C2×D43 | semidirect |
| 160. C42 | C2×D43 | semidirect |
| 161. C42 | C2×D43 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13063320 | 2 |
| #13063319 | 2 |
| #13063313 | 2 |
| #13063310 | 2 |
| #13063308 | 2 |
| #13063303 | 2 |
| #13063302 | 2 |
| #13063295 | 2 |
| C4×D172 | 2 |
| (C22⋊D43)⋊C4 | 2 |
| #13063282 | 2 |
| C2×(C2×D43)⋊C4 | 2 |
| C22⋊C4×D43 | 2 |
| #117×C43 | 2 |
| #551 | 43 |