Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1045 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 1045 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. C2×#88538 | C2 | semidirect |
| 4. #11720531 | C2 | semidirect |
| 10. C2×C4⋊#272 | C4 | semidirect |
| 12. C4⋊C4×H(3,𝔽3) | C22 | semidirect |
| 16. C2×#6180 | C22 | semidirect |
| 18. C32×#117 | D3 | semidirect |
| 42. C32×C4⋊C4 | C2×D3 | semidirect |
| 117. #117 | #272 | semidirect |
| 119. H(3,𝔽3) | #418 | semidirect |
| 158. C4⋊C4 | C2×#272 | semidirect |
| 181. C32 | #5001 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊#272 | 2 |
| H(3,𝔽3)×#117 | 2 |
| C2×#88538 | 2 |
| #11720531 | 2 |
| C3×#5001 | 3 |