Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
226 conjugacy classes of subgroups; only the 124 normal subgroups are shown.
This group has 226 conjugacy classes of subgroups — too many to draw. Only its 124 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×#3667 | C2 | semidirect |
| 3. C2×C3×C9⋊C8 | C2 | semidirect |
| 5. #63510 | C3 | direct (N × H) |
| 16. #3667 | C2×C3 | semidirect |
| 17. C2×C9⋊C8 | C2×C3 | semidirect |
| 55. C3×C9 | #131 | semidirect |
| 89. C9 | C3×#131 | semidirect |
| 105. C3 | #63510 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#41 | 2 |
| C3×#3667 | 2 |
| C2×C3×C9⋊C8 | 2 |
| C3×#948 | 3 |
| #63510 | 3 |