Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
512 conjugacy classes of subgroups; only the 193 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 193 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | D4×D43 |
| commutator | C4×C43 | C2×C42 |
| Frattini | C22×C4 | C22×D43 |
| Fitting | C43×#340 | C2 |
| socle | C23×C43 | C2×D4 |
| hypercenter | #340 | D43 |
| hypocenter | C43 | C2×#340 |
| LCS | G ▷ C4×C43 ▷ C2×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ C22×C4 ◁ #340 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582662 | C2 | semidirect |
| 4. #14582661 | C2 | semidirect |
| 5. C43×#340 | C2 | semidirect |
| 10. C2×C8×D43 | C4 | semidirect |
| 14. C4⋊C4×D43 | C4 | semidirect |
| 30. C2×C8×C43 | C2×C4 | semidirect |
| 32. C4⋊C4×C43 | C2×C4 | semidirect |
| 34. C4⋊Dic43 | C2×C4 | semidirect |
| 37. C2×C43⋊C8 | C2×C4 | semidirect |
| 85. D43 | #340 | direct (N × H) |
| 90. #340 | D43 | direct (N × H) |
| 91. C43 | C2×#340 | semidirect |
| 119. C2×C8 | C4×D43 | semidirect |
| 124. C4⋊C4 | C4×D43 | semidirect |