Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
217 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 217 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 |
|---|---|---|
| 4. #10589672 | C3 | semidirect |
| 17. C9×SL(2,𝔽3) | Q8 | semidirect |
| 102. SL(2,𝔽3) | Dic18 | semidirect |
| 135. C9 | #557⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C9×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×Dic9 | 2 |
| #5570⋊C3 | 3 |
| #10589672 | 3 |
| C3×C4⋊Dic9 | 4 |