Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 147 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. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 4. #11720506 | C2 | semidirect |
| 5. C16×C3⋊D9 | C2 | semidirect |
| 22. C9×M32 | D3 | semidirect |
| 59. C3×M32 | D9 | semidirect |
| 115. M32 | C3⋊D9 | semidirect |
| 118. C3×C9 | #504 | semidirect |
| 160. C9 | #4907 | semidirect |
| 180. C3 | #10588587 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721770 | 2 |
| C3×C9×M32 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| #11720506 | 2 |
| C16×C3⋊D9 | 2 |
| #10592606 | 3 |
| #10588587 | 3 |