Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
158 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 158 conjugacy classes of subgroups — too many to draw. Only its 57 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. C3×C9×M16 | C2 | semidirect |
| 3. C9×#208 | C2 | semidirect |
| 18. C9×M16 | D3 | semidirect |
| 25. #823 | C9 | direct (N × H) |
| 47. C3×M16 | C2×C9 | semidirect |
| 49. #208 | C2×C9 | semidirect |
| 64. C3×C9 | #100 | semidirect |
| 89. M16 | D3×C9 | semidirect |
| 105. C9 | #823 | direct (N × H) |
| 126. C3 | C9×#100 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D12 | 2 |
| C3×C9×M16 | 2 |
| C9×#208 | 2 |
| C3×#823 | 3 |
| C9×#100 | 3 |