Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1976 conjugacy classes of subgroups; only the 645 normal subgroups are shown.
This group has 1976 conjugacy classes of subgroups — too many to draw. Only its 645 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 | C4×C43 | C25 |
| Frattini | C4 | C24×D43 |
| Fitting | C23×D4×C43 | C2 |
| socle | C24×C43 | D4 |
| hypercenter | C23×D4 | D43 |
| hypocenter | C43 | C23×D8 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C24 ◁ C23×C4 ◁ C23×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C23×D172 | C2 | semidirect |
| 2. C22×#10621882 | C2 | direct (N × H) |
| 3. C23×C43⋊C8 | C2 | semidirect |
| 4. C23×D4×C43 | C2 | semidirect |
| 7. C22×D172 | C22 | semidirect |
| 8. C2×#10621882 | C22 | direct (N × H) |
| 9. C22×C43⋊C8 | C22 | semidirect |
| 12. C22×D4×C43 | C22 | semidirect |
| 20. C2×D4×C43 | C23 | semidirect |
| 24. C2×D172 | C23 | semidirect |
| 25. #10621882 | C23 | direct (N × H) |
| 26. C2×C43⋊C8 | C23 | semidirect |
| 29. C23×C43 | D8 | semidirect |
| 34. D4×C43 | C24 | semidirect |
| 38. D172 | C24 | semidirect |
| 39. C43⋊C8 | C24 | semidirect |
| 42. C22×C43 | C2×D8 | semidirect |
| 50. C2×C43 | C22×D8 | semidirect |
| 54. C23×D4 | D43 | semidirect |
| 57. C43 | C23×D8 | semidirect |
| 63. C22×D4 | C2×D43 | semidirect |
| 75. C2×D4 | C22×D43 | semidirect |
| 84. C23 | #10621882 | direct (N × H) |
| 89. D4 | C23×D43 | semidirect |
| 97. C22 | C2×#10621882 | direct (N × H) |
| 103. C2 | C22×#10621882 | direct (N × H) |