Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
272 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 272 conjugacy classes of subgroups — too many to draw. Only its 40 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. C3×#63771 | C2 | semidirect |
| 3. C3×#63764 | C2 | semidirect |
| 4. #10590198 | C3 | direct (N × H) |
| 14. #63771 | C2×C3 | semidirect |
| 15. #63764 | C2×C3 | semidirect |
| 96. C33 | #359 | semidirect |
| 142. C32 | C3×#359 | semidirect |
| 165. C3 | #10590198 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64128 | 2 |
| C3×#63771 | 2 |
| C3×#63764 | 2 |
| #10590198 | 3 |
| C3×#359 | 9 |