Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
6520 conjugacy classes of subgroups; only the 3301 normal subgroups are shown.
This group has 6520 conjugacy classes of subgroups — too many to draw. Only its 3301 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C22×D43 |
| commutator | C2×C43 | C26 |
| Frattini | C2 | C25×D43 |
| Fitting | C23×D4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C23×D4 | D43 |
| hypocenter | C43 | C23×#41 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#10621900 | C2 | direct (N × H) |
| 2. C23×Dic86 | C2 | semidirect |
| 3. C23×C22⋊D43 | C2 | semidirect |
| 4. C24×Dic43 | C2 | semidirect |
| 5. C23×C4×D43 | C2 | semidirect |
| 6. C23×D4×C43 | C2 | semidirect |
| 8. C2×#10621900 | C22 | direct (N × H) |
| 9. C22×Dic86 | C22 | semidirect |
| 10. C22×C22⋊D43 | C22 | semidirect |
| 13. C23×Dic43 | C22 | semidirect |
| 14. C22×C4×D43 | C22 | semidirect |
| 16. C22×D4×C43 | C22 | semidirect |
| 23. C2×D4×C43 | C23 | semidirect |
| 25. C2×C22⋊D43 | C23 | semidirect |
| 28. C22×Dic43 | C23 | semidirect |
| 29. #10621900 | C23 | direct (N × H) |
| 30. C2×C4×D43 | C23 | semidirect |
| 31. C2×Dic86 | C23 | semidirect |
| 33. C23×C43 | #41 | semidirect |
| 38. D4×C43 | C24 | semidirect |
| 40. C22⋊D43 | C24 | semidirect |
| 43. C2×Dic43 | C24 | semidirect |
| 44. C4×D43 | C24 | semidirect |
| 45. Dic86 | C24 | semidirect |
| 47. C22×C43 | C2×#41 | semidirect |
| 57. C2×C43 | C22×#41 | semidirect |
| 63. C23×D4 | D43 | semidirect |
| 66. C43 | C23×#41 | semidirect |
| 72. C22×D4 | C2×D43 | semidirect |
| 86. C2×D4 | C22×D43 | semidirect |
| 95. C23 | #10621900 | direct (N × H) |
| 100. D4 | C23×D43 | semidirect |
| 109. C22 | C2×#10621900 | direct (N × H) |
| 117. C2 | C22×#10621900 | direct (N × H) |