Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
1504 conjugacy classes of subgroups; only the 1077 normal subgroups are shown.
This group has 1504 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 | C22×C4 | C22×D43 |
| commutator | C2×C43 | C24×C4 |
| Frattini | C4 | C24×D43 |
| Fitting | C22×#41×C43 | C2 |
| socle | C23×C43 | C22×C4 |
| hypercenter | C22×#41 | D43 |
| hypocenter | C43 | C22×#131 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#13063332 | C2 | direct (N × H) |
| 2. C22×#10621877 | C2 | semidirect |
| 3. C23×C43⋊C8 | C2 | semidirect |
| 5. #13063332 | C22 | direct (N × H) |
| 6. C2×#10621877 | C22 | semidirect |
| 9. C22×C43⋊C8 | C22 | semidirect |
| 24. #10621877 | C23 | semidirect |
| 27. C2×C43⋊C8 | C23 | semidirect |
| 41. C22×C43 | #131 | semidirect |
| 49. C2×C43 | C2×#131 | semidirect |
| 55. C43 | C22×#131 | semidirect |
| 92. C22 | #13063332 | direct (N × H) |
| 99. C2 | C2×#13063332 | direct (N × H) |