Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
1016 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 1016 conjugacy classes of subgroups — too many to draw. Only its 198 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×#64153 | C2 | semidirect |
| 3. C2×C3×#3756 | C2 | semidirect |
| 6. C2×C3×#3746 | C2 | semidirect |
| 7. C3×#63642 | C2 | semidirect |
| 8. #10592866 | C3 | direct (N × H) |
| 26. #64153 | C2×C3 | semidirect |
| 27. C2×#3756 | C2×C3 | semidirect |
| 30. C2×#3746 | C2×C3 | semidirect |
| 36. #63642 | C2×C3 | semidirect |
| 215. C33 | #497 | semidirect |
| 303. C32 | #5167 | semidirect |
| 304. C32 | C3×#497 | semidirect |
| 340. C3 | C3×#5167 | semidirect |
| 341. C3 | #10592866 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C33×SD16 | 2 |
| C3×#64153 | 2 |
| C2×C3×#3756 | 2 |
| C3×#64145 | 2 |
| C2×C3×#3754 | 2 |
| C2×C3×#3746 | 2 |
| C3×#63642 | 2 |
| #10592866 | 3 |
| C3×#5167 | 3 |