Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
181 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 181 conjugacy classes of subgroups — too many to draw. Only its 35 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 |
|---|---|---|
| 3. C9×#395 | C3 | semidirect |
| 4. #395⋊C9 | C3 | semidirect |
| 14. #395⋊C3 | C9 | direct (N × H) |
| 41. #395 | C3×C9 | semidirect |
| 94. C9 | #395⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×C22⋊SL(2,𝔽3) | 2 |
| C3×#395⋊C3 | 3 |
| C9×#395 | 3 |
| #395⋊C9 | 3 |
| C4×C9×A4 | 4 |