Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
291 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 291 conjugacy classes of subgroups — too many to draw. Only its 91 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×Q16 | C3 | semidirect |
| 5. Q16×C22⋊C9 | C3 | semidirect |
| 22. A4×Q16 | C9 | direct (N × H) |
| 37. C9×Q16 | A4 | direct (N × H) |
| 40. C9×A4 | Q16 | direct (N × H) |
| 67. C22×Q16 | C3×C9 | semidirect |
| 88. C22×C9 | C3×Q16 | semidirect |
| 89. C22⋊C9 | C3×Q16 | semidirect |
| 129. Q16 | C9×A4 | direct (N × H) |
| 135. A4 | C9×Q16 | direct (N × H) |
| 144. C9 | A4×Q16 | direct (N × H) |
| 162. C22 | C3×C9×Q16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| C8×C9×A4 | 2 |
| C3×A4×Q16 | 3 |
| C22×C9×Q16 | 3 |
| Q16×C22⋊C9 | 3 |
| C3×C9×Q16 | 4 |