Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 71 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×C3×Dic18 | C2 | semidirect |
| 3. C2×C3⋊(C9⋊C8) | C2 | semidirect |
| 4. #88423 | C2 | direct (N × H) |
| 13. C3×Dic18 | C22 | semidirect |
| 14. C3⋊(C9⋊C8) | C22 | semidirect |
| 20. C2×Dic18 | D3 | semidirect |
| 47. Dic18 | C2×D3 | semidirect |
| 50. C2×C3×C9 | SD16 | semidirect |
| 78. C3×C9 | C2×SD16 | semidirect |
| 103. C2×C9 | #215 | semidirect |
| 126. C9 | C2×#215 | semidirect |
| 138. C2×C3 | #3672 | semidirect |
| 150. C3 | C2×#3672 | semidirect |
| 153. C2 | #88423 | 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×C3×Dic18 | 2 |
| C2×C3⋊(C9⋊C8) | 2 |
| #88423 | 2 |
| C2×#3715 | 3 |
| C2×#3672 | 3 |