Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
119 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 119 conjugacy classes of subgroups — too many to draw. Only its 50 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 |
|---|---|---|
| 3. C22×C9×C16 | C3 | semidirect |
| 4. C16×C22⋊C9 | C3 | semidirect |
| 24. C9×C16 | A4 | semidirect |
| 25. C9⋊A4 | C16 | direct (N × H) |
| 40. C22×C16 | 3−1+2 | semidirect |
| 53. C22×C9 | C3×C16 | semidirect |
| 54. C22⋊C9 | C3×C16 | semidirect |
| 78. C16 | C9⋊A4 | direct (N × H) |
| 88. C9 | A4×C16 | semidirect |
| 100. C22 | C16×3−1+2 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C9⋊A4 | 2 |
| C3×A4×C16 | 3 |
| C22×C9×C16 | 3 |
| C16×C22⋊C9 | 3 |
| C16×3−1+2 | 4 |