Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
438 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 438 conjugacy classes of subgroups — too many to draw. Only its 106 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×#63432 | C2 | semidirect |
| 3. C3×#63392 | C2 | semidirect |
| 4. C3×#63362 | C2 | semidirect |
| 6. #10588751 | C3 | direct (N × H) |
| 19. #63432 | C2×C3 | semidirect |
| 20. #63392 | C2×C3 | semidirect |
| 21. #63362 | C2×C3 | semidirect |
| 120. C3×C9 | #490 | semidirect |
| 174. C9 | C3×#490 | semidirect |
| 198. C3 | #10588751 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#127 | 2 |
| C3×#63432 | 2 |
| C3×#63392 | 2 |
| C3×#63362 | 2 |
| C3×#5071 | 3 |
| #10588751 | 3 |