Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
243 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 243 conjugacy classes of subgroups — too many to draw. Only its 45 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 |
|---|---|---|
| 5. C22×#3674 | C3 | semidirect |
| 46. #3674 | A4 | direct (N × H) |
| 49. C9×A4 | Q16 | semidirect |
| 117. C22×C9 | C3×Q16 | semidirect |
| 183. A4 | #3674 | direct (N × H) |
| 197. C9 | A4×Q16 | semidirect |
| 222. C22 | C3×#3674 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×C9×A4 | 2 |
| A4×Dic18 | 2 |
| A4×C9⋊C8 | 2 |
| A4×#216 | 3 |
| C22×#3674 | 3 |
| C3×#3674 | 4 |