Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
869 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 159 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 |
|---|---|---|
| 2. H(3,𝔽3)×#117 | C2 | semidirect |
| 3. #11721826 | C2 | semidirect |
| 4. #11720524 | C2 | semidirect |
| 12. C2×C4⋊#272 | C4 | semidirect |
| 13. C2×C4×#272 | C4 | semidirect |
| 14. C2×#6229 | C4 | semidirect |
| 22. C32×#117 | D3 | semidirect |
| 152. #117 | #272 | semidirect |
| 154. H(3,𝔽3) | #410 | semidirect |
| 239. C32 | #5006 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88740 | 2 |
| H(3,𝔽3)×#117 | 2 |
| #11721826 | 2 |
| #11720524 | 2 |
| C3×#5006 | 3 |