Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
699 conjugacy classes of subgroups; only the 208 normal subgroups are shown.
This group has 699 conjugacy classes of subgroups — too many to draw. Only its 208 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 |
|---|---|---|
| 4. #10592347 | C3 | semidirect |
| 9. C4×(C3⋊Dic3)⋊C3 | C4 | semidirect |
| 34. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 105. H(3,𝔽3) | #376 | semidirect |
| 166. C32 | #4648 | semidirect |
| 167. C32 | C3×#376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×(C3⋊Dic3)⋊C3 | 2 |
| H(3,𝔽3)×#95 | 2 |
| #63658⋊C3 | 2 |
| #10592347 | 3 |
| C3×#4648 | 3 |