Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
744 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 744 conjugacy classes of subgroups — too many to draw. Only its 170 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 |
|---|---|---|
| 3. C33×#103 | C2 | semidirect |
| 4. C3×#63662 | C2 | semidirect |
| 6. C3×#63645 | C2 | semidirect |
| 7. C3×#63635 | C2 | semidirect |
| 8. #10592513 | C3 | direct (N × H) |
| 26. C32×#103 | D3 | semidirect |
| 27. C32×#103 | C2×C3 | semidirect |
| 28. #63662 | C2×C3 | semidirect |
| 30. #63645 | C2×C3 | semidirect |
| 31. #63635 | C2×C3 | semidirect |
| 95. C3×#103 | C3×D3 | semidirect |
| 96. C3×#103 | C3⋊D3 | semidirect |
| 196. #103 | C3×C3⋊D3 | semidirect |
| 198. C33 | #485 | semidirect |
| 281. C32 | #4814 | semidirect |
| 282. C32 | C3×#485 | semidirect |
| 319. C3 | C3×#4814 | semidirect |
| 320. C3 | #10592513 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64155 | 2 |
| C3×#64101 | 2 |
| C33×#103 | 2 |
| C3×#63662 | 2 |
| C3×#63647 | 2 |
| C3×#63645 | 2 |
| C3×#63635 | 2 |
| #10592513 | 3 |
| C3×#4814 | 3 |