Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
242 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 242 conjugacy classes of subgroups — too many to draw. Only its 57 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 | semidirect |
| 5. C9×#41⋊C3 | C4 | semidirect |
| 7. C2×C9×SL(2,𝔽3) | C4 | semidirect |
| 20. #5423 | C9 | direct (N × H) |
| 50. GU(2,𝔽3) | C2×C9 | semidirect |
| 84. #41⋊C3 | C4×C9 | semidirect |
| 87. C2×SL(2,𝔽3) | C4×C9 | semidirect |
| 173. C9 | #5423 | 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 |
| C3×#5423 | 3 |
| C9×#421 | 3 |
| C9×#208 | 4 |