Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
643 conjugacy classes of subgroups; only the 143 normal subgroups are shown.
This group has 643 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 |
|---|---|---|
| 2. C2×C4×C9×A4 | C2 | semidirect |
| 4. C22×C9×C22⋊C4 | C3 | semidirect |
| 5. C22⋊C4×C22⋊C9 | C3 | semidirect |
| 7. C22×C9×A4 | C4 | semidirect |
| 15. C23×C4×C9 | C2×C3 | semidirect |
| 16. C2×C4×C22⋊C9 | C2×C3 | semidirect |
| 26. A4×C22⋊C4 | C9 | direct (N × H) |
| 36. C24×C9 | C3×C4 | semidirect |
| 39. C22×C22⋊C9 | C3×C4 | semidirect |
| 51. C9×C22⋊C4 | A4 | direct (N × H) |
| 55. C9×A4 | C22⋊C4 | direct (N × H) |
| 60. C2×C4×A4 | C2×C9 | semidirect |
| 98. C2×C4×C9 | C2×A4 | semidirect |
| 99. C22×C22⋊C4 | C3×C9 | semidirect |
| 111. C22×A4 | C4×C9 | semidirect |
| 147. C22×C9 | C3×C22⋊C4 | semidirect |
| 148. C22×C9 | C4×A4 | semidirect |
| 150. C22⋊C9 | C3×C22⋊C4 | semidirect |
| 155. C23×C4 | C2×C3×C9 | semidirect |
| 208. C24 | C3×C4×C9 | semidirect |
| 217. C22⋊C4 | C9×A4 | direct (N × H) |
| 240. A4 | C9×C22⋊C4 | direct (N × H) |
| 246. C9 | A4×C22⋊C4 | direct (N × H) |
| 271. C2×C4 | C2×C9×A4 | semidirect |
| 298. C22 | C3×C9×C22⋊C4 | semidirect |
| 299. C22 | C4×C9×A4 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C9×A4 | 2 |
| C2×C4×C9×A4 | 2 |
| C3×A4×C22⋊C4 | 3 |
| C22×C9×C22⋊C4 | 3 |
| C22⋊C4×C22⋊C9 | 3 |
| C3×C9×C22⋊C4 | 4 |