Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
410 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 131 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. C2×#88521 | C2 | semidirect |
| 3. C3×C9×M32 | C2 | semidirect |
| 4. #11720509 | C2 | semidirect |
| 5. #11720508 | C2 | semidirect |
| 24. C9×M32 | D3 | semidirect |
| 67. C3×M32 | D9 | semidirect |
| 131. M32 | C3⋊D9 | semidirect |
| 132. C3×C9 | #510 | semidirect |
| 181. C9 | #4909 | semidirect |
| 204. C3 | #10588589 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11721773 | 2 |
| C2×#88521 | 2 |
| C3×C9×M32 | 2 |
| #11720509 | 2 |
| #11720508 | 2 |
| #10592608 | 3 |
| #10588589 | 3 |