Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
144 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 144 conjugacy classes of subgroups — too many to draw. Only its 65 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×C22⋊D43 |
| commutator | C4×C43 | C22×C8 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C43×#504 | C2 |
| socle | C2×C43 | C8×D4 |
| hypercenter | #504 | D43 |
| hypocenter | C43 | #2171 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C8 ◁ C2×C16 ◁ #504 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #14583315 | C2 | semidirect |
| 3. #14582719 | C2 | semidirect |
| 4. #14582684 | C2 | semidirect |
| 5. #14582683 | C2 | semidirect |
| 6. #14582674 | C2 | semidirect |
| 7. C43×#504 | C2 | semidirect |
| 73. #504 | D43 | semidirect |
| 79. C43 | #2171 | semidirect |