Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1011 conjugacy classes of subgroups; only the 420 normal subgroups are shown.
This group has 1011 conjugacy classes of subgroups — too many to draw. Only its 420 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 |
|---|---|---|
| 3. C42×C3⋊Dic3 | C3 | semidirect |
| 7. C42×H(3,𝔽3) | C4 | semidirect |
| 8. C4×(C3⋊Dic3)⋊C3 | C4 | direct (N × H) |
| 27. C32×C42 | Dic3 | semidirect |
| 28. C32×C42 | C3×C4 | semidirect |
| 29. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 33. C4×H(3,𝔽3) | C42 | semidirect |
| 34. (C3⋊Dic3)⋊C3 | C42 | direct (N × H) |
| 77. C32×C4 | C4×Dic3 | semidirect |
| 78. C32×C4 | C3×C42 | semidirect |
| 79. C3⋊Dic3 | C3×C42 | semidirect |
| 83. H(3,𝔽3) | C43 | semidirect |
| 108. C42 | (C3⋊Dic3)⋊C3 | direct (N × H) |
| 125. C32 | C42×Dic3 | semidirect |
| 126. C32 | C3×C43 | semidirect |
| 142. C4 | C4×(C3⋊Dic3)⋊C3 | direct (N × H) |
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 |
| C42×C3⋊Dic3 | 3 |
| C3×C42×Dic3 | 3 |