Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
168 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 87 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4 | C42×D43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C2×C8 | C22×D43 |
| Fitting | C43×#347 | C2 |
| socle | C2×C43 | C2×#97 |
| hypercenter | #347 | D43 |
| hypocenter | C43 | C2×#347 |
| LCS | G ▷ C4×C43 ▷ C43 | |
| UCS | C1 ◁ C4 ◁ #347 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582677 | C2 | semidirect |
| 4. #14582676 | C2 | semidirect |
| 5. C43×#347 | C2 | semidirect |
| 10. #13063264 | C4 | semidirect |
| 11. C16×D43 | C4 | semidirect |
| 30. C16×C43 | C2×C4 | semidirect |
| 31. C43⋊C16 | C2×C4 | semidirect |
| 60. D43 | #347 | direct (N × H) |
| 65. #347 | D43 | direct (N × H) |
| 66. C43 | C2×#347 | semidirect |
| 92. C16 | C4×D43 | semidirect |