Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 386 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 |
|---|---|---|
| 1. C3×C9×#131 | C2 | semidirect |
| 2. C3×#63512 | C2 | semidirect |
| 3. C2×C3×D72 | C2 | semidirect |
| 4. C3×#63383 | C2 | semidirect |
| 5. C3×#63372 | C2 | semidirect |
| 7. #10588823 | C3 | direct (N × H) |
| 25. C9×#131 | C2×C3 | semidirect |
| 26. #63512 | C2×C3 | semidirect |
| 27. C2×D72 | C2×C3 | semidirect |
| 28. #63383 | C2×C3 | semidirect |
| 29. #63372 | C2×C3 | semidirect |
| 81. C3×#131 | D9 | semidirect |
| 174. #131 | C3×D9 | semidirect |
| 177. C3×C9 | #472 | semidirect |
| 253. C9 | C3×#472 | semidirect |
| 285. C3 | #10588823 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#131 | 2 |
| C3×#63512 | 2 |
| C2×C3×D72 | 2 |
| C3×#63383 | 2 |
| C3×#63372 | 2 |
| C3×#5142 | 3 |
| #10588823 | 3 |