Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
672 conjugacy classes of subgroups; only the 294 normal subgroups are shown.
This group has 672 conjugacy classes of subgroups — too many to draw. Only its 294 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. C32×C4⋊Dic3 | C2 | semidirect |
| 4. C32×C4×Dic3 | C2 | semidirect |
| 6. C3×#926 | C3 | direct (N × H) |
| 8. C2×C33×C4 | C4 | semidirect |
| 19. C3×C4⋊Dic3 | C2×C3 | semidirect |
| 20. C3×C4×Dic3 | C2×C3 | semidirect |
| 28. #926 | C32 | direct (N × H) |
| 36. C2×C32×C4 | Dic3 | semidirect |
| 37. C2×C32×C4 | C3×C4 | semidirect |
| 53. C4⋊Dic3 | C2×C32 | semidirect |
| 54. C4×Dic3 | C2×C32 | semidirect |
| 73. C33 | #117 | semidirect |
| 81. C2×C3×C4 | C3×Dic3 | semidirect |
| 82. C2×C3×C4 | C32×C4 | semidirect |
| 119. C32 | #926 | direct (N × H) |
| 120. C32 | C3×#117 | semidirect |
| 123. C2×C4 | C32×Dic3 | semidirect |
| 142. C3 | C3×#926 | direct (N × H) |
| 143. C3 | C32×#117 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C33×C4 | 2 |
| C32×#217 | 2 |
| C32×C4⋊Dic3 | 2 |
| C32×C4×Dic3 | 2 |
| C32×#117 | 3 |
| C3×#926 | 3 |