Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
731 conjugacy classes of subgroups; only the 244 normal subgroups are shown.
This group has 731 conjugacy classes of subgroups — too many to draw. Only its 244 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. #10592631 | C3 | semidirect |
| 9. C42×H(3,𝔽3) | C4 | semidirect |
| 10. C4×(C3⋊Dic3)⋊C3 | C4 | semidirect |
| 37. C32×C42 | Dic3 | semidirect |
| 38. C32×C42 | C3×C4 | semidirect |
| 39. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 118. H(3,𝔽3) | #376 | semidirect |
| 158. C42 | (C3⋊Dic3)⋊C3 | semidirect |
| 183. C32 | #4932 | semidirect |
| 184. C32 | C3×#376 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C42×H(3,𝔽3) | 2 |
| C2×C4×(C3⋊Dic3)⋊C3 | 2 |
| #63658⋊C3 | 2 |
| #10592631 | 3 |
| C3×#4932 | 3 |