Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
583 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 583 conjugacy classes of subgroups — too many to draw. Only its 81 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×C9×SL(2,ℤ/4) | C2 | semidirect |
| 6. C22×C9×A4 | C4 | semidirect |
| 23. #5432 | C9 | direct (N × H) |
| 34. C24×C9 | Dic3 | semidirect |
| 51. C9×A4 | C22⋊C4 | semidirect |
| 56. C2×SL(2,ℤ/4) | C2×C9 | semidirect |
| 110. C22×A4 | C4×C9 | semidirect |
| 146. C22×C9 | #217 | semidirect |
| 147. C22×C9 | SL(2,ℤ/4) | semidirect |
| 210. C24 | C9×Dic3 | semidirect |
| 246. A4 | C9×C22⋊C4 | semidirect |
| 252. C9 | #5432 | direct (N × H) |
| 307. C22 | C9×#217 | semidirect |
| 308. C22 | C9×SL(2,ℤ/4) | 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×C9×SL(2,ℤ/4) | 2 |
| C3×#5432 | 3 |
| C9×#379 | 3 |
| C9×#217 | 4 |