Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
332 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | #13063297 |
| commutator | C2×C4×C43 | C22×C4 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#421 | C2 |
| socle | C2×C43 | #386 |
| hypercenter | #421 | D43 |
| hypocenter | C43 | #1906 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ C22×C4 ◁ #421 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #41×Dic43 | C2 | semidirect |
| 3. C2×#13063251 | C2 | semidirect |
| 4. #14582872 | C2 | semidirect |
| 5. #14582670 | C2 | semidirect |
| 6. #14582658 | C2 | semidirect |
| 7. C43×#421 | C2 | semidirect |
| 10. #13063355 | C4 | semidirect |
| 12. #13063350 | C4 | semidirect |
| 45. C2×D172 | C2×C4 | semidirect |
| 47. C2×Dic86 | C2×C4 | semidirect |
| 68. #10621877 | C2×C4 | semidirect |
| 132. #421 | D43 | semidirect |
| 137. C43 | #1906 | semidirect |