Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 226 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×#41 | C2 | semidirect |
| 2. C9×#235 | C2 | semidirect |
| 3. C9×#216 | C2 | semidirect |
| 4. C9×#215 | C2 | semidirect |
| 5. C9×#214 | C2 | semidirect |
| 6. C9×#213 | C2 | semidirect |
| 7. C2×C9×C3⋊C8 | C2 | semidirect |
| 30. C9×#41 | D3 | semidirect |
| 44. #950 | C9 | direct (N × H) |
| 78. C3×#41 | C2×C9 | semidirect |
| 80. #235 | C2×C9 | semidirect |
| 86. #216 | C2×C9 | semidirect |
| 87. #215 | C2×C9 | semidirect |
| 88. #214 | C2×C9 | semidirect |
| 89. #213 | C2×C9 | semidirect |
| 90. C2×C3⋊C8 | C2×C9 | semidirect |
| 111. C3×C9 | #135 | semidirect |
| 151. #41 | D3×C9 | semidirect |
| 178. C9 | #950 | direct (N × H) |
| 209. C3 | C9×#135 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#41 | 2 |
| C9×#235 | 2 |
| C9×#216 | 2 |
| C9×#215 | 2 |
| C9×#214 | 2 |
| C9×#213 | 2 |
| C2×C9×C3⋊C8 | 2 |
| C3×#950 | 3 |
| C9×#135 | 3 |