Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
168 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 168 conjugacy classes of subgroups — too many to draw. Only its 66 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. #10589372 | C3 | semidirect |
| 74. H(3,𝔽3) | #368 | semidirect |
| 112. C32 | #4506 | semidirect |
| 113. C32 | C3×#368 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C16×H(3,𝔽3) | 2 |
| #63646⋊C3 | 2 |
| #10589372 | 3 |
| C3×#4506 | 3 |