Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
300 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 300 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. #10589914 | C3 | semidirect |
| 5. C2×C9×SL(2,𝔽3) | C4 | semidirect |
| 13. Q8×Dic9 | C2×C3 | semidirect |
| 26. C2×Q8×C9 | C3×C4 | semidirect |
| 76. C2×SL(2,𝔽3) | Dic9 | semidirect |
| 133. C2×Q8 | C3×Dic9 | semidirect |
| 159. C9 | #519⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×Dic9 | 2 |
| #5812⋊C3 | 3 |
| #10589914 | 3 |
| C3×#3676 | 4 |