Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
904 conjugacy classes of subgroups; only the 164 normal subgroups are shown.
This group has 904 conjugacy classes of subgroups — too many to draw. Only its 164 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. C32×#803 | C2 | semidirect |
| 4. #11722042 | C2 | semidirect |
| 20. #64078 | D3 | semidirect |
| 25. C3×#803 | D3 | semidirect |
| 82. #803 | C3⋊D3 | semidirect |
| 169. C33 | #489 | semidirect |
| 245. C32 | #4714 | semidirect |
| 246. C32 | #5089 | semidirect |
| 279. C3 | #10590294 | semidirect |
| 280. C3 | #10592413 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11723916 | 2 |
| C3×#64078 | 2 |
| C32×#803 | 2 |
| #11722042 | 2 |
| #11722036 | 2 |
| #10592413 | 3 |
| #10590294 | 3 |