Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
517 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 517 conjugacy classes of subgroups — too many to draw. Only its 147 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 |
|---|---|---|
| 8. C42×H(3,𝔽3) | C4 | semidirect |
| 11. C4×#1084 | C4 | semidirect |
| 14. C2×#6180 | C4 | semidirect |
| 33. C32×C42 | Dic3 | semidirect |
| 104. H(3,𝔽3) | H(3,ℤ/4) | semidirect |
| 138. C42 | #1084 | semidirect |
| 159. C32 | #4531 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#117 | 2 |
| #11721826 | 2 |
| C2×#88538 | 2 |
| C3×#4531 | 3 |