Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
320 conjugacy classes of subgroups; only the 87 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 87 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×C22⋊C8 | C2 | semidirect |
| 3. C9×C3⋊#95 | C2 | semidirect |
| 9. C2×C9×D12 | C4 | semidirect |
| 12. C9×C4⋊Dic3 | C4 | semidirect |
| 18. C9×C22⋊C8 | D3 | semidirect |
| 34. #4470 | C9 | direct (N × H) |
| 66. C3×C22⋊C8 | C2×C9 | semidirect |
| 69. C3⋊#95 | C2×C9 | semidirect |
| 116. C2×D12 | C4×C9 | semidirect |
| 123. C4⋊Dic3 | C4×C9 | semidirect |
| 156. C22⋊C8 | D3×C9 | semidirect |
| 158. C3×C9 | #327 | semidirect |
| 247. C9 | #4470 | direct (N × H) |
| 291. C3 | C9×#327 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#930 | 2 |
| C3×C9×C22⋊C8 | 2 |
| C9×C3⋊#95 | 2 |
| C3×#4470 | 3 |
| C9×#327 | 3 |