Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
336 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 336 conjugacy classes of subgroups — too many to draw. Only its 105 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. C2×C3×D4×C9 | C2 | semidirect |
| 2. C2×C9×#67 | C2 | semidirect |
| 3. C2×C4×D3×C9 | C2 | semidirect |
| 4. C9×#217 | C2 | semidirect |
| 5. C9×C4⋊Dic3 | C2 | semidirect |
| 23. C2×D4×C9 | D3 | semidirect |
| 33. C2×D3×C9 | D4 | semidirect |
| 34. C3×C4×C9 | D4 | semidirect |
| 38. #938 | C9 | direct (N × H) |
| 65. C2×C3×D4 | C2×C9 | semidirect |
| 68. C2×#67 | C2×C9 | semidirect |
| 69. C2×C4×D3 | C2×C9 | semidirect |
| 72. #217 | C2×C9 | semidirect |
| 73. C4⋊Dic3 | C2×C9 | semidirect |
| 98. C4×C9 | #67 | semidirect |
| 100. C3×C9 | #121 | semidirect |
| 135. C2×D4 | D3×C9 | semidirect |
| 156. C2×D3 | D4×C9 | semidirect |
| 160. C3×C4 | D4×C9 | semidirect |
| 166. C9 | #938 | direct (N × H) |
| 198. C4 | C9×#67 | semidirect |
| 200. C3 | C9×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C9×#67 | 2 |
| C2×C4×D3×C9 | 2 |
| C9×#217 | 2 |
| C9×C4⋊Dic3 | 2 |
| C3×#938 | 3 |
| C9×#121 | 3 |