Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
265 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 265 conjugacy classes of subgroups — too many to draw. Only its 58 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. Dic9⋊SL(2,𝔽3) | C2 | semidirect |
| 4. #10589929 | C3 | semidirect |
| 5. #88683 | C4 | semidirect |
| 18. C9⋊SL(2,𝔽3) | C2×C4 | semidirect |
| 25. C9×#41 | C3×C4 | semidirect |
| 128. #41 | 3−1+2⋊C4 | semidirect |
| 152. C9 | #520⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88683 | 2 |
| Dic9⋊SL(2,𝔽3) | 2 |
| #5827⋊C3 | 3 |
| #10589929 | 3 |
| C4⋊(3−1+2⋊C4) | 4 |