Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1880 conjugacy classes of subgroups; only the 1157 normal subgroups are shown.
This group has 1880 conjugacy classes of subgroups — too many to draw. Only its 1157 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 | C24×C4×C43 | C2 |
| socle | C24×C43 | C23 |
| hypercenter | C24×C4 | D43 |
| hypocenter | C43 | C22×#117 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23×C4 ◁ C24×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063284 | C2 | direct (N × H) |
| 2. C22×C4⋊Dic43 | C2 | semidirect |
| 4. C22×C4×Dic43 | C2 | semidirect |
| 7. #13063284 | C22 | direct (N × H) |
| 8. C2×C4⋊Dic43 | C22 | semidirect |
| 10. C2×C4×Dic43 | C22 | semidirect |
| 12. C23×C4×C43 | C4 | semidirect |
| 22. C22×C4×C43 | C2×C4 | semidirect |
| 29. C4⋊Dic43 | C23 | semidirect |
| 30. C4×Dic43 | C23 | semidirect |
| 40. C2×C4×C43 | C22×C4 | semidirect |
| 47. C22×C43 | #117 | semidirect |
| 57. C2×C43 | C2×#117 | semidirect |
| 65. C43 | C22×#117 | semidirect |
| 68. C23×C4 | Dic43 | semidirect |
| 84. C22×C4 | C2×Dic43 | semidirect |
| 102. C2×C4 | C22×Dic43 | semidirect |
| 107. C22 | #13063284 | direct (N × H) |
| 116. C2 | C2×#13063284 | direct (N × H) |