Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 258 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. C9×#214 | C2 | direct (N × H) |
| 4. C2×C9×C3⋊C8 | C2 | semidirect |
| 13. C9×Dic6 | C22 | semidirect |
| 14. C9×C3⋊C8 | C22 | semidirect |
| 31. C2×#214 | C9 | direct (N × H) |
| 53. C2×C3×C9 | SD16 | semidirect |
| 59. C2×Dic6 | C2×C9 | semidirect |
| 62. #214 | C2×C9 | direct (N × H) |
| 63. C2×C3⋊C8 | C2×C9 | semidirect |
| 82. C3×C9 | C2×SD16 | semidirect |
| 100. Dic6 | C22×C9 | semidirect |
| 102. C3⋊C8 | C22×C9 | semidirect |
| 110. C2×C9 | #214 | direct (N × H) |
| 135. C9 | C2×#214 | direct (N × H) |
| 149. C2×C3 | C9×SD16 | semidirect |
| 160. C3 | C2×C9×SD16 | semidirect |
| 163. C2 | C9×#214 | direct (N × H) |
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×Dic6 | 2 |
| C9×#214 | 2 |
| C2×C9×C3⋊C8 | 2 |
| C2×C3×#214 | 3 |
| C2×C9×SD16 | 3 |