Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
220 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 220 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 |
|---|---|---|
| 2. C2×C9×Dic6 | C2 | semidirect |
| 3. C9×#216 | C2 | semidirect |
| 4. C9×#214 | C2 | semidirect |
| 5. C9×#208 | C2 | semidirect |
| 35. #951 | C9 | direct (N × H) |
| 66. C2×Dic6 | C2×C9 | semidirect |
| 70. #216 | C2×C9 | semidirect |
| 71. #214 | C2×C9 | semidirect |
| 72. #208 | C2×C9 | semidirect |
| 91. C3×C9 | #137 | semidirect |
| 148. C9 | #951 | direct (N × H) |
| 174. C3 | C9×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#41 | 2 |
| C2×C9×Dic6 | 2 |
| C9×#216 | 2 |
| C9×#214 | 2 |
| C9×#208 | 2 |
| C3×#951 | 3 |
| C9×#137 | 3 |