Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
302 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 302 conjugacy classes of subgroups — too many to draw. Only its 147 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. C3×C9×C4⋊C4 | C2 | semidirect |
| 4. C9×C4⋊Dic3 | C2 | semidirect |
| 5. C9×Dic3⋊C4 | C2 | semidirect |
| 14. C4×D3×C9 | C4 | semidirect |
| 25. C9×C4⋊C4 | D3 | direct (N × H) |
| 31. C3×C4×C9 | C2×C4 | semidirect |
| 33. C9×Dic3 | C2×C4 | semidirect |
| 35. D3×C4⋊C4 | C9 | direct (N × H) |
| 55. D3×C9 | C4⋊C4 | direct (N × H) |
| 63. C3×C4⋊C4 | C2×C9 | semidirect |
| 65. C4⋊Dic3 | C2×C9 | semidirect |
| 66. Dic3⋊C4 | C2×C9 | semidirect |
| 85. C4×C9 | C4×D3 | semidirect |
| 87. C3×C9 | C2×C4⋊C4 | semidirect |
| 103. C4×D3 | C4×C9 | semidirect |
| 119. C4⋊C4 | D3×C9 | direct (N × H) |
| 135. C3×C4 | C2×C4×C9 | semidirect |
| 138. Dic3 | C2×C4×C9 | semidirect |
| 141. C9 | D3×C4⋊C4 | direct (N × H) |
| 159. D3 | C9×C4⋊C4 | direct (N × H) |
| 167. C4 | C4×D3×C9 | semidirect |
| 169. C3 | C2×C9×C4⋊C4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C3×C9×C4⋊C4 | 2 |
| C9×C4⋊Dic3 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×D3×C4⋊C4 | 3 |
| C2×C9×C4⋊C4 | 3 |