Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
156 conjugacy classes of subgroups; only the 73 normal subgroups are shown.
This group has 156 conjugacy classes of subgroups — too many to draw. Only its 73 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C43⋊#95 |
| commutator | C2×C4×C43 | C42 |
| Frattini | C2×C42 | C2×D43 |
| Fitting | C43×#382 | C2 |
| socle | C22×C43 | #95 |
| hypercenter | #382 | D43 |
| hypocenter | C43 | #1286 |
| LCS | G ▷ C2×C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C22 ◁ C2×C42 ◁ #382 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 7. C4⋊(C43⋊C8) | C4 | semidirect |
| 9. C4×C43⋊C8 | C4 | semidirect |
| 69. C43 | #1286 | semidirect |