Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×C3×C8×C9 | C2 | semidirect |
| 4. C9×#204 | C2 | direct (N × H) |
| 13. C9×Dic6 | C22 | semidirect |
| 14. C3×C8×C9 | C22 | semidirect |
| 23. C2×C8×C9 | D3 | semidirect |
| 31. C2×#204 | C9 | direct (N × H) |
| 49. C8×C9 | C2×D3 | semidirect |
| 50. C2×C3×C9 | SD16 | semidirect |
| 56. C2×Dic6 | C2×C9 | semidirect |
| 59. C2×C3×C8 | C2×C9 | semidirect |
| 61. #204 | C2×C9 | direct (N × H) |
| 78. C3×C9 | C2×SD16 | semidirect |
| 93. Dic6 | C22×C9 | semidirect |
| 95. C3×C8 | C22×C9 | semidirect |
| 103. C2×C9 | #204 | direct (N × H) |
| 108. C2×C8 | D3×C9 | semidirect |
| 126. C9 | C2×#204 | direct (N × H) |
| 134. C8 | C2×D3×C9 | semidirect |
| 138. C2×C3 | C9×SD16 | semidirect |
| 150. C3 | C2×C9×SD16 | semidirect |
| 153. C2 | C9×#204 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C2×C9×Dic6 | 2 |
| C2×C3×C8×C9 | 2 |
| C9×#204 | 2 |
| C2×C3×#204 | 3 |
| C2×C9×SD16 | 3 |