Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
168 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 109 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C4×Dic43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C2×#97×C43 | C2 |
| socle | C22×C43 | #97 |
| hypercenter | C2×#97 | D43 |
| hypocenter | C43 | C2×#347 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#97 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14582677 | C2 | direct (N × H) |
| 4. #13063265 | C4 | semidirect |
| 6. C2×C43⋊C16 | C4 | semidirect |
| 23. C43⋊C16 | C2×C4 | semidirect |
| 48. C2×C43 | #347 | semidirect |
| 53. C43 | C2×#347 | semidirect |
| 97. C2 | #14582677 | direct (N × H) |