Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1880 conjugacy classes of subgroups; only the 901 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 901 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23×C4 | C2×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C22 | C24×D43 |
| Fitting | C22×C42×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C22×C42 | D43 |
| hypocenter | C43 | C22×#117 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23×C4 ◁ C22×C42 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#13063282 | C2 | direct (N × H) |
| 3. C22×Dic43⋊C4 | C2 | semidirect |
| 5. C22×C4×Dic43 | C2 | semidirect |
| 6. C22×C42×C43 | C2 | semidirect |
| 10. C22×C4×D43 | C4 | semidirect |
| 12. #13063282 | C22 | direct (N × H) |
| 13. C2×Dic43⋊C4 | C22 | semidirect |
| 15. C2×C4×Dic43 | C22 | semidirect |
| 18. C2×C42×C43 | C22 | semidirect |
| 31. C2×C4×D43 | C2×C4 | semidirect |
| 33. C42×C43 | C23 | semidirect |
| 35. Dic43⋊C4 | C23 | semidirect |
| 36. C4×Dic43 | C23 | semidirect |
| 52. C4×D43 | C22×C4 | semidirect |
| 53. C22×C43 | #117 | semidirect |
| 65. C2×C43 | C2×#117 | semidirect |
| 74. C22×C42 | D43 | semidirect |
| 75. C43 | C22×#117 | semidirect |
| 87. C2×C42 | C2×D43 | semidirect |
| 105. C42 | C22×D43 | semidirect |
| 125. C22 | #13063282 | direct (N × H) |
| 134. C2 | C2×#13063282 | direct (N × H) |