Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
228 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 1. C2×C9⋊(C22⋊C9) | C2 | semidirect |
| 2. D9⋊(C22⋊C9) | C2 | direct (N × H) |
| 6. C9⋊(C22⋊C9) | C22 | semidirect |
| 18. C23×D9 | C9 | semidirect |
| 39. C23×C9 | C2×C9 | semidirect |
| 43. C22×D9 | C2×C9 | semidirect |
| 72. C22×C9 | C22×C9 | semidirect |
| 78. C2×D9 | C22⋊C9 | semidirect |
| 108. C2×C9 | C2×C22⋊C9 | semidirect |
| 110. D9 | C2×C22⋊C9 | semidirect |
| 137. C9 | C22×C22⋊C9 | semidirect |
| 142. C23 | D9⋊C9 | semidirect |
| 164. C22 | C2×D9⋊C9 | semidirect |
| 172. C2 | D9⋊(C22⋊C9) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊(C22⋊C9) | 2 |
| D9⋊(C22⋊C9) | 2 |
| C23×C3×D9 | 3 |
| C2×D3×C22⋊C9 | 3 |
| C2×D9⋊C9 | 4 |