Finite Group DatabasebetaFinite Group DatabasebetaOrder 576.
566 conjugacy classes of subgroups; only the 148 normal subgroups are shown.
This group has 566 conjugacy classes of subgroups — too many to draw. Only its 148 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #64286 | C2 | direct (N × H) |
| 4. C2×C4⋊#157 | C2 | semidirect |
| 5. C2×C4×#157 | C2 | semidirect |
| 8. C22×C32×C4 | C4 | semidirect |
| 9. C22×C3⋊Dic3 | C4 | semidirect |
| 10. C2×C4×C3⋊D3 | C4 | semidirect |
| 11. C2×C4×C3⋊D3 | C4 | semidirect |
| 12. C2×C4×C3⋊D3 | C4 | semidirect |
| 17. C4⋊#157 | C22 | semidirect |
| 18. C4×#157 | C22 | semidirect |
| 30. C2×C32×C4 | C2×C4 | semidirect |
| 33. C2×C3⋊Dic3 | C2×C4 | semidirect |
| 36. C4×C3⋊D3 | C2×C4 | semidirect |
| 37. C4×C3⋊D3 | C2×C4 | semidirect |
| 89. C2×C32 | #117 | semidirect |
| 92. C3⋊D3 | #117 | semidirect |
| 103. C22×C4 | #157 | semidirect |
| 121. C32 | C2×#117 | semidirect |
| 141. C2×C4 | C2×#157 | semidirect |
| 168. C2 | #64286 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×C3⋊D3 | 2 |
| C2×C22⋊#157 | 2 |
| #64286 | 2 |
| C2×C4⋊#157 | 2 |
| C2×C4×#157 | 2 |
| C2×#117 | 9 |