Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
278 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 278 conjugacy classes of subgroups — too many to draw. Only its 63 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. SL(2,𝔽3)×Dic9 | C2 | semidirect |
| 4. #10589929 | C3 | semidirect |
| 5. C9×#41⋊C3 | C4 | semidirect |
| 18. C9×SL(2,𝔽3) | C2×C4 | semidirect |
| 25. C9×#41 | C3×C4 | semidirect |
| 76. #41⋊C3 | Dic9 | semidirect |
| 121. SL(2,𝔽3) | C2×Dic9 | semidirect |
| 133. #41 | C3×Dic9 | semidirect |
| 159. C9 | #520⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41⋊C3 | 2 |
| SL(2,𝔽3)×Dic9 | 2 |
| #5827⋊C3 | 3 |
| #10589929 | 3 |
| C3×C4⋊Dic9 | 4 |