Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
132 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 77 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C8 | (C2×D43)⋊C4 |
| commutator | C22×C43 | C4×C8 |
| Frattini | C22×C8 | C2×D43 |
| Fitting | C43×#405 | C2 |
| socle | C2×C43 | #336 |
| hypercenter | #405 | D43 |
| hypocenter | C43 | #1378 |
| LCS | G ▷ C22×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C22×C8 ◁ #405 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. #13063265 | C4 | semidirect |
| 9. C2×C43⋊C16 | C4 | semidirect |
| 60. C43 | #1378 | semidirect |