Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
223 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 223 conjugacy classes of subgroups — too many to draw. Only its 51 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 |
|---|---|---|
| 7. C9×#226 | C4 | semidirect |
| 24. #5388 | C9 | direct (N × H) |
| 81. #226 | C4×C9 | semidirect |
| 165. C9 | #5388 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#226 | 2 |
| C4×C9×SL(2,𝔽3) | 2 |
| C9×#859 | 2 |
| C3×#5388 | 3 |
| C9×#441 | 3 |
| C9×Dic3⋊C4 | 4 |