Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
620 conjugacy classes of subgroups; only the 174 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 174 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×#63639 | C2 | semidirect |
| 3. #10589419 | C3 | direct (N × H) |
| 13. #63639 | C2×C3 | semidirect |
| 108. C33 | #349 | semidirect |
| 163. C32 | #4553 | semidirect |
| 164. C32 | C3×#349 | semidirect |
| 188. C3 | C3×#4553 | semidirect |
| 189. C3 | #10589419 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×M16 | 2 |
| C3×#63639 | 2 |
| #10589419 | 3 |
| C3×#4553 | 3 |