Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
397 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 397 conjugacy classes of subgroups — too many to draw. Only its 114 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. #10589423 | C3 | semidirect |
| 7. C2×C8×H(3,𝔽3) | C4 | semidirect |
| 10. C4×(C3⋊Dic3)⋊C3 | C4 | semidirect |
| 33. C2×C32×C8 | Dic3 | semidirect |
| 34. C2×C32×C8 | C3×C4 | semidirect |
| 37. C4×C3⋊Dic3 | C3×C4 | semidirect |
| 122. H(3,𝔽3) | H(3,ℤ/4) | semidirect |
| 161. C2×C8 | (C3⋊Dic3)⋊C3 | semidirect |
| 193. C32 | #4557 | semidirect |
| 194. C32 | C3×H(3,ℤ/4) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×H(3,𝔽3) | 2 |
| #64135⋊C3 | 2 |
| #10589423 | 3 |
| C3×#4557 | 3 |