Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
450 conjugacy classes of subgroups; only the 149 normal subgroups are shown.
This group has 450 conjugacy classes of subgroups — too many to draw. Only its 149 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 |
| 4. #11720506 | C2 | semidirect |
| 5. C16×C3⋊D9 | C2 | semidirect |
| 15. C3×C9×C16 | C22 | semidirect |
| 16. C3⋊(C9⋊C16) | C22 | semidirect |
| 23. C9×M32 | D3 | semidirect |
| 56. C9×C16 | C2×D3 | semidirect |
| 68. C3×M32 | D9 | semidirect |
| 102. C3⋊D9 | M32 | direct (N × H) |
| 117. C3×C16 | C2×D9 | semidirect |
| 140. M32 | C3⋊D9 | direct (N × H) |
| 142. C3×C9 | C2×M32 | semidirect |
| 181. C16 | C2×C3⋊D9 | semidirect |
| 199. C9 | D3×M32 | semidirect |
| 227. C3 | D9×M32 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×C3⋊D9 | 2 |
| C3×C9×M32 | 2 |
| #11720534 | 2 |
| #11720506 | 2 |
| C16×C3⋊D9 | 2 |
| C3⋊D3×M32 | 3 |
| D9×M32 | 3 |