Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 93 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 |
|---|---|---|
| 2. C2×C4×D3×C9 | C2 | semidirect |
| 3. C3×C9×C4⋊C4 | C2 | semidirect |
| 4. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C9×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C9×Dic3⋊C4 | C2 | semidirect |
| 30. C9×C4⋊C4 | D3 | semidirect |
| 47. #894 | C9 | direct (N × H) |
| 77. C2×C4×D3 | C2×C9 | semidirect |
| 80. C3×C4⋊C4 | C2×C9 | semidirect |
| 85. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 86. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 87. (C2×D3)⋊C4 | C2×C9 | semidirect |
| 88. Dic3⋊C4 | C2×C9 | semidirect |
| 118. C3×C9 | #123 | semidirect |
| 156. C4⋊C4 | D3×C9 | semidirect |
| 190. C9 | #894 | direct (N × H) |
| 226. C3 | C9×#123 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C2×C4×D3×C9 | 2 |
| C3×C9×C4⋊C4 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C9×Dic3⋊C4 | 2 |
| C3×#894 | 3 |
| C9×#123 | 3 |