Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
904 conjugacy classes of subgroups; only the 234 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 234 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. C32×#869 | C2 | semidirect |
| 3. C32×#835 | C2 | semidirect |
| 5. C32×#803 | C2 | semidirect |
| 7. C3×#5055 | C3 | direct (N × H) |
| 21. C3×#869 | C2×C3 | semidirect |
| 25. C3×#835 | C2×C3 | semidirect |
| 27. C3×#803 | C2×C3 | semidirect |
| 39. #5055 | C32 | direct (N × H) |
| 76. #869 | C2×C32 | semidirect |
| 80. #835 | C2×C32 | semidirect |
| 82. #803 | C2×C32 | semidirect |
| 169. C33 | #489 | semidirect |
| 245. C32 | #5055 | direct (N × H) |
| 246. C32 | C3×#489 | semidirect |
| 279. C3 | C3×#5055 | direct (N × H) |
| 280. C3 | C32×#489 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#124 | 2 |
| C32×#869 | 2 |
| C32×#835 | 2 |
| C32×#832 | 2 |
| C32×#803 | 2 |
| C32×#489 | 3 |
| C3×#5055 | 3 |