Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
489 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 489 conjugacy classes of subgroups — too many to draw. Only its 122 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. #10592361 | C3 | semidirect |
| 99. H(3,𝔽3) | #401 | semidirect |
| 159. C32 | C3⋊#401 | semidirect |
| 160. C32 | C3×#401 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×#95 | 2 |
| #63658⋊C3 | 2 |
| #10592361 | 3 |
| C3×C3⋊#401 | 3 |