Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
720 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 720 conjugacy classes of subgroups — too many to draw. Only its 179 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. C3⋊(C3⋊GU(2,𝔽3)) | C2 | semidirect |
| 5. C32×#41⋊C3 | C4 | semidirect |
| 7. C2×C32×SL(2,𝔽3) | C4 | semidirect |
| 28. C3×#41⋊C3 | Dic3 | semidirect |
| 30. C2×C3×SL(2,𝔽3) | Dic3 | semidirect |
| 75. #41⋊C3 | C3⋊Dic3 | semidirect |
| 77. C2×SL(2,𝔽3) | C3⋊Dic3 | semidirect |
| 152. C32 | #5423 | semidirect |
| 183. C3 | #10593657 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41⋊C3 | 2 |
| C3⋊(C3⋊GU(2,𝔽3)) | 2 |
| #10593657 | 3 |
| #10592935 | 3 |
| #88855 | 4 |