Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
187 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 187 conjugacy classes of subgroups — too many to draw. Only its 74 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. #10589378 | C3 | semidirect |
| 9. C16×H(3,𝔽3) | C4 | semidirect |
| 10. (C3⋊(C3⋊C16))⋊C3 | C4 | semidirect |
| 34. C32×C16 | Dic3 | semidirect |
| 35. C32×C16 | C3×C4 | semidirect |
| 36. C3⋊(C3⋊C16) | C3×C4 | semidirect |
| 99. H(3,𝔽3) | #347 | semidirect |
| 128. C16 | (C3⋊Dic3)⋊C3 | semidirect |
| 145. C32 | #4512 | semidirect |
| 146. C32 | C3×#347 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×M32 | 2 |
| #63642⋊C3 | 2 |
| #63639⋊C3 | 2 |
| #10589378 | 3 |
| C3×#4512 | 3 |