Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
206 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 87 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 |
|---|---|---|
| 1. C3×C9×C4⋊C4 | C2 | semidirect |
| 5. C9×C4⋊Dic3 | C2 | semidirect |
| 6. C9×Dic3⋊C4 | C2 | semidirect |
| 7. C4×C9×Dic3 | C2 | semidirect |
| 27. C9×C4⋊C4 | D3 | semidirect |
| 43. #898 | C9 | direct (N × H) |
| 68. C3×C4⋊C4 | C2×C9 | semidirect |
| 77. C4⋊Dic3 | C2×C9 | semidirect |
| 78. Dic3⋊C4 | C2×C9 | semidirect |
| 79. C4×Dic3 | C2×C9 | semidirect |
| 105. C3×C9 | #126 | semidirect |
| 136. C4⋊C4 | D3×C9 | semidirect |
| 167. C9 | #898 | direct (N × H) |
| 197. C3 | C9×#126 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C4⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×C4⋊Dic3 | 2 |
| C9×Dic3⋊C4 | 2 |
| C4×C9×Dic3 | 2 |
| C3×#898 | 3 |
| C9×#126 | 3 |