Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
266 conjugacy classes of subgroups; only the 98 normal subgroups are shown.
This group has 266 conjugacy classes of subgroups — too many to draw. Only its 98 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×#64218 | C2 | direct (N × H) |
| 3. C2×C3×#3771 | C2 | semidirect |
| 4. C2×#64218 | C3 | direct (N × H) |
| 10. C3×#3771 | C22 | semidirect |
| 12. #64218 | C2×C3 | direct (N × H) |
| 13. C2×#3771 | C2×C3 | semidirect |
| 29. #3771 | C22×C3 | semidirect |
| 55. C2×C33 | M32 | semidirect |
| 82. C33 | C2×M32 | semidirect |
| 104. C2×C32 | C3×M32 | semidirect |
| 129. C32 | C2×C3×M32 | semidirect |
| 145. C2×C3 | #64218 | direct (N × H) |
| 155. C3 | C2×#64218 | direct (N × H) |
| 157. C2 | C3×#64218 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#622 | 2 |
| C3×#64218 | 2 |
| C2×C3×#3771 | 2 |
| C2×#64218 | 3 |
| C2×C3×M32 | 9 |