Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
572 conjugacy classes of subgroups; only the 381 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 381 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C42 | C22×D43 |
| commutator | C2×C43 | C22×C42 |
| Frattini | C2×C4 | C23×D43 |
| Fitting | C4×#41×C43 | C2 |
| socle | C22×C43 | C23×C4 |
| hypercenter | C4×#41 | D43 |
| hypocenter | C43 | C4×#131 |
| LCS | G ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C42 ◁ C4×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582855 | C2 | semidirect |
| 3. C4×#10621877 | C2 | semidirect |
| 4. C2×C4×C43⋊C8 | C2 | semidirect |
| 6. #13063332 | C4 | direct (N × H) |
| 28. #10621877 | C2×C4 | semidirect |
| 29. C2×C43⋊C8 | C2×C4 | semidirect |
| 48. C4×C43 | #131 | semidirect |
| 59. C43 | C4×#131 | semidirect |
| 102. C4 | #13063332 | direct (N × H) |