Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
330 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 195 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. C9×C4⋊Dic3 | C2 | direct (N × H) |
| 7. C2×C3×C4×C9 | C4 | semidirect |
| 22. C3×C4×C9 | C2×C4 | semidirect |
| 25. C2×C4⋊Dic3 | C9 | direct (N × H) |
| 37. C2×C4×C9 | Dic3 | semidirect |
| 39. C2×C3×C9 | C4⋊C4 | semidirect |
| 49. C4⋊Dic3 | C2×C9 | direct (N × H) |
| 66. C4×C9 | C2×Dic3 | semidirect |
| 68. C3×C9 | C2×C4⋊C4 | semidirect |
| 76. C2×C3×C4 | C4×C9 | semidirect |
| 90. C2×C9 | C4⋊Dic3 | direct (N × H) |
| 111. C3×C4 | C2×C4×C9 | semidirect |
| 116. C9 | C2×C4⋊Dic3 | direct (N × H) |
| 120. C2×C4 | C9×Dic3 | semidirect |
| 126. C2×C3 | C9×C4⋊C4 | semidirect |
| 139. C4 | C2×C9×Dic3 | semidirect |
| 141. C3 | C2×C9×C4⋊C4 | semidirect |
| 143. C2 | C9×C4⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C22×C9×Dic3 | 2 |
| C9×C4⋊Dic3 | 2 |
| C2×C3×C4⋊Dic3 | 3 |
| C2×C9×C4⋊C4 | 3 |