Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
810 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 191 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⋊#859) | C2 | semidirect |
| 5. C32×#41⋊C3 | C4 | semidirect |
| 17. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 21. C32×#41 | Dic3 | semidirect |
| 26. C3×#41⋊C3 | Dic3 | semidirect |
| 56. C3×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 63. C3×#41 | C3⋊Dic3 | semidirect |
| 68. #41⋊C3 | C3⋊Dic3 | semidirect |
| 105. SL(2,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 115. #41 | C3⋊(C3⋊Dic3) | semidirect |
| 136. C32 | #5426 | semidirect |
| 165. C3 | #10593660 | 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⋊#859) | 2 |
| #10593660 | 3 |
| #10592931 | 3 |
| C4⋊(C3⋊(C3⋊Dic3)) | 4 |