Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1920 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1920 conjugacy classes of subgroups — too many to draw. Only its 1077 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C23×D4×C43 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | C23×D4 | D43 |
| hypocenter | C43 | C2×#518 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583374 | C2 | direct (N × H) |
| 2. C2×D4×Dic43 | C2 | semidirect |
| 3. C2×#13063284 | C2 | semidirect |
| 4. C22×C22⋊Dic43 | C2 | semidirect |
| 6. C23×Dic43 | C22 | semidirect |
| 7. D4×Dic43 | C22 | semidirect |
| 8. #13063284 | C22 | semidirect |
| 9. C2×C4⋊Dic43 | C22 | semidirect |
| 11. C2×C22⋊Dic43 | C22 | semidirect |
| 12. C2×C22⋊Dic43 | C22 | semidirect |
| 13. C2×C4×Dic43 | C22 | semidirect |
| 15. C22×D4×C43 | C4 | semidirect |
| 20. C24×C43 | C2×C4 | semidirect |
| 24. C2×D4×C43 | C2×C4 | semidirect |
| 25. C2×D4×C43 | C2×C4 | semidirect |
| 27. C22×C4×C43 | C2×C4 | semidirect |
| 32. C22×Dic43 | C23 | semidirect |
| 34. C22⋊Dic43 | C23 | semidirect |
| 35. C4⋊Dic43 | C23 | semidirect |
| 36. C4×Dic43 | C23 | semidirect |
| 43. C23×C43 | C22×C4 | semidirect |
| 47. D4×C43 | C22×C4 | semidirect |
| 49. C2×C4×C43 | C22×C4 | semidirect |
| 69. C2×C43 | #518 | semidirect |
| 77. C43 | C2×#518 | semidirect |
| 79. C22×D4 | Dic43 | semidirect |
| 92. C24 | C2×Dic43 | semidirect |
| 96. C2×D4 | C2×Dic43 | semidirect |
| 97. C2×D4 | C2×Dic43 | semidirect |
| 102. C22×C4 | C2×Dic43 | semidirect |
| 115. C23 | C22×Dic43 | semidirect |
| 119. D4 | C22×Dic43 | semidirect |
| 124. C2×C4 | C22×Dic43 | semidirect |
| 140. C2 | #14583374 | direct (N × H) |