Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
848 conjugacy classes of subgroups; only the 190 normal subgroups are shown.
This group has 848 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 |
|---|---|---|
| 3. C2×C3×#3746 | C2 | semidirect |
| 4. C3×#63651 | C2 | semidirect |
| 5. C3×#63646 | C2 | semidirect |
| 6. #10592842 | C3 | direct (N × H) |
| 23. C2×#3746 | C2×C3 | semidirect |
| 26. #63651 | C2×C3 | semidirect |
| 27. #63646 | C2×C3 | semidirect |
| 173. C33 | #473 | semidirect |
| 244. C32 | #5143 | semidirect |
| 245. C32 | C3×#473 | semidirect |
| 274. C3 | C3×#5143 | semidirect |
| 275. C3 | #10592842 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×#131 | 2 |
| C3×#64160 | 2 |
| C2×C3×#3746 | 2 |
| C3×#63651 | 2 |
| C3×#63646 | 2 |
| #10592842 | 3 |
| C3×#5143 | 3 |