Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
538 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 90 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. C2×C3×#3777 | C2 | semidirect |
| 3. C3×#63747 | C2 | semidirect |
| 4. #10593566 | C3 | direct (N × H) |
| 11. C2×#3777 | C2×C3 | semidirect |
| 12. #63747 | C2×C3 | semidirect |
| 89. C33 | #399 | semidirect |
| 142. C32 | C3×#399 | semidirect |
| 175. C3 | #10593566 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C22⋊#157 | 2 |
| C2×C3×#3777 | 2 |
| C3×#63747 | 2 |
| #10593566 | 3 |
| C3×#399 | 9 |