Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
269 conjugacy classes of subgroups; only the 63 normal subgroups are shown.
This group has 269 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. C9×GU(2,𝔽3) | C2 | direct (N × H) |
| 5. C9×#41⋊C3 | C4 | semidirect |
| 7. C2×C9×SL(2,𝔽3) | C4 | semidirect |
| 18. C9×SL(2,𝔽3) | C2×C4 | semidirect |
| 20. C2×GU(2,𝔽3) | C9 | direct (N × H) |
| 50. GU(2,𝔽3) | C2×C9 | direct (N × H) |
| 86. #41⋊C3 | C4×C9 | semidirect |
| 89. C2×SL(2,𝔽3) | C4×C9 | semidirect |
| 134. SL(2,𝔽3) | C2×C4×C9 | semidirect |
| 143. C2×C9 | GU(2,𝔽3) | direct (N × H) |
| 175. C9 | C2×GU(2,𝔽3) | direct (N × H) |
| 213. C2 | C9×GU(2,𝔽3) | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×#41⋊C3 | 2 |
| C9×GU(2,𝔽3) | 2 |
| C2×C3×GU(2,𝔽3) | 3 |
| C2×C9×#104 | 3 |
| C2×C9×C3⋊C8 | 4 |