Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
328 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 122 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. C3×Dic9⋊C8 | C2 | semidirect |
| 5. C3×C4×C9⋊C8 | C2 | semidirect |
| 7. #10588390 | C3 | direct (N × H) |
| 22. C9×#97 | C2×C3 | semidirect |
| 24. Dic9⋊C8 | C2×C3 | semidirect |
| 25. C4×C9⋊C8 | C2×C3 | semidirect |
| 64. C3×#97 | D9 | semidirect |
| 129. #97 | C3×D9 | semidirect |
| 131. C3×C9 | #433 | semidirect |
| 185. C9 | C3×#433 | semidirect |
| 210. C3 | #10588390 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63434 | 2 |
| C3×C9×#97 | 2 |
| C3×(C2×D9)⋊C8 | 2 |
| C3×Dic9⋊C8 | 2 |
| C3×C4×C9⋊C8 | 2 |
| C3×#4709 | 3 |
| #10588390 | 3 |