Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
904 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 190 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×#64078 | C2 | semidirect |
| 3. C3×#63662 | C2 | semidirect |
| 5. C3×#63630 | C2 | semidirect |
| 6. #10592754 | C3 | direct (N × H) |
| 20. #64078 | C2×C3 | semidirect |
| 22. #63662 | C2×C3 | semidirect |
| 24. #63630 | C2×C3 | semidirect |
| 169. C33 | #489 | semidirect |
| 245. C32 | #5055 | semidirect |
| 246. C32 | C3×#489 | semidirect |
| 279. C3 | C3×#5055 | semidirect |
| 280. C3 | #10592754 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#124 | 2 |
| C3×#64078 | 2 |
| C3×#63662 | 2 |
| C3×#63659 | 2 |
| C3×#63630 | 2 |
| #10592754 | 3 |
| C3×#5055 | 3 |