Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
328 conjugacy classes of subgroups; only the 141 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 141 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×#97 | C2 | semidirect |
| 4. C9×Dic3⋊C8 | C2 | semidirect |
| 5. C4×C9×C3⋊C8 | C2 | semidirect |
| 24. C9×#97 | D3 | semidirect |
| 35. #4709 | C9 | direct (N × H) |
| 64. C3×#97 | C2×C9 | semidirect |
| 68. Dic3⋊C8 | C2×C9 | semidirect |
| 69. C4×C3⋊C8 | C2×C9 | semidirect |
| 129. #97 | D3×C9 | semidirect |
| 131. C3×C9 | #433 | semidirect |
| 185. C9 | #4709 | direct (N × H) |
| 210. C3 | C9×#433 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#872 | 2 |
| C3×C9×#97 | 2 |
| C9×(C2×D3)⋊C8 | 2 |
| C9×Dic3⋊C8 | 2 |
| C4×C9×C3⋊C8 | 2 |
| C3×#4709 | 3 |
| C9×#433 | 3 |