Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
188 conjugacy classes of subgroups; only the 50 normal subgroups are shown.
This group has 188 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 |
|---|---|---|
| 2. C22×C32×C16 | C3 | semidirect |
| 3. C3×A4×C16 | C3 | semidirect |
| 21. C32×C16 | A4 | semidirect |
| 22. C22⋊H(3,𝔽3) | C16 | direct (N × H) |
| 38. C22×C16 | H(3,𝔽3) | semidirect |
| 54. C22×C32 | C3×C16 | semidirect |
| 55. C3×A4 | C3×C16 | semidirect |
| 83. C16 | C22⋊H(3,𝔽3) | direct (N × H) |
| 97. C32 | A4×C16 | semidirect |
| 112. C22 | C16×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C8×C22⋊H(3,𝔽3) | 2 |
| C22×C32×C16 | 3 |
| C3×A4×C16 | 3 |
| C16×H(3,𝔽3) | 4 |