Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
869 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 869 conjugacy classes of subgroups — too many to draw. Only its 173 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. C22×#6180 | C2 | semidirect |
| 4. #11720532 | C2 | semidirect |
| 5. #11720531 | C2 | semidirect |
| 10. #88740 | C4 | semidirect |
| 20. C32×#117 | D3 | semidirect |
| 129. #117 | #272 | semidirect |
| 132. H(3,𝔽3) | #416 | semidirect |
| 199. C32 | #5002 | 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 |
| C22×#6180 | 2 |
| #11720532 | 2 |
| #11720531 | 2 |
| C3×#5002 | 3 |