Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
443 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 443 conjugacy classes of subgroups — too many to draw. Only its 143 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 |
|---|---|---|
| 4. C22×C9×C4⋊C4 | C3 | semidirect |
| 5. C4⋊C4×C22⋊C9 | C3 | semidirect |
| 8. C4×C9×A4 | C4 | semidirect |
| 25. A4×C4⋊C4 | C9 | direct (N × H) |
| 39. C22×C4×C9 | C3×C4 | semidirect |
| 41. C4×C22⋊C9 | C3×C4 | semidirect |
| 46. C9×C4⋊C4 | A4 | direct (N × H) |
| 48. C9×A4 | C4⋊C4 | direct (N × H) |
| 87. C22×C4⋊C4 | C3×C9 | semidirect |
| 102. C4×A4 | C4×C9 | semidirect |
| 123. C22×C9 | C3×C4⋊C4 | semidirect |
| 125. C22⋊C9 | C3×C4⋊C4 | semidirect |
| 131. C4×C9 | C4×A4 | semidirect |
| 183. C22×C4 | C3×C4×C9 | semidirect |
| 187. C4⋊C4 | C9×A4 | direct (N × H) |
| 201. A4 | C9×C4⋊C4 | direct (N × H) |
| 210. C9 | A4×C4⋊C4 | direct (N × H) |
| 250. C22 | C3×C9×C4⋊C4 | semidirect |
| 255. C4 | C4×C9×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C9×A4 | 2 |
| C3×A4×C4⋊C4 | 3 |
| C22×C9×C4⋊C4 | 3 |
| C4⋊C4×C22⋊C9 | 3 |
| C3×C9×C4⋊C4 | 4 |