Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
290 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 290 conjugacy classes of subgroups — too many to draw. Only its 107 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. C3×C9×M32 | C2 | semidirect |
| 3. #11720534 | C2 | semidirect |
| 17. C9×M32 | D3 | semidirect |
| 51. C3×M32 | D9 | semidirect |
| 103. M32 | C3⋊D9 | semidirect |
| 104. C3×C9 | #349 | semidirect |
| 147. C9 | #4514 | semidirect |
| 168. C3 | #10588191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88523 | 2 |
| C3×C9×M32 | 2 |
| #11720534 | 2 |
| #10589380 | 3 |
| #10588191 | 3 |