Finite Group DatabasebetaFinite Group DatabasebetaOrder 5504.
888 conjugacy classes of subgroups; only the 365 normal subgroups are shown.
This group has 888 conjugacy classes of subgroups — too many to draw. Only its 365 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×D43 |
| commutator | C22×C43 | C23×C4 |
| Fitting | C43×#384 | C2 |
| socle | C23×C43 | C24 |
| hypercenter | #384 | D43 |
| hypocenter | C43 | C2×#384 |
| LCS | G ▷ C22×C43 ▷ C43 | |
| UCS | C1 ◁ C23 ◁ #384 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #14582769 | C2 | semidirect |
| 4. #14582768 | C2 | semidirect |
| 5. C43×#384 | C2 | semidirect |
| 12. C42×D43 | C4 | semidirect |
| 25. C42×C43 | C2×C4 | semidirect |
| 28. C4×Dic43 | C2×C4 | semidirect |
| 42. C4×D43 | C4⋊C4 | semidirect |
| 50. C4×C43 | C2×C4⋊C4 | semidirect |
| 52. Dic43 | C2×C4⋊C4 | semidirect |
| 57. D43 | #384 | direct (N × H) |
| 62. #384 | D43 | direct (N × H) |
| 63. C43 | C2×#384 | semidirect |
| 86. C42 | C4×D43 | semidirect |
| 110. C4 | C4⋊C4×D43 | semidirect |