Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
230 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 78 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×#63372 | C2 | semidirect |
| 3. C2×C3×C9⋊C16 | C2 | semidirect |
| 5. #10588244 | C3 | direct (N × H) |
| 18. #63372 | C2×C3 | semidirect |
| 19. C2×C9⋊C16 | C2×C3 | semidirect |
| 125. C3×C9 | #359 | semidirect |
| 182. C9 | C3×#359 | semidirect |
| 206. C3 | #10588244 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#135 | 2 |
| C3×#63372 | 2 |
| C2×C3×C9⋊C16 | 2 |
| C3×#4567 | 3 |
| #10588244 | 3 |