Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
212 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 70 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. C3×#63372 | C2 | semidirect |
| 5. #10588193 | C3 | direct (N × H) |
| 17. C9×M32 | C2×C3 | semidirect |
| 18. #63372 | C2×C3 | semidirect |
| 50. C3×M32 | D9 | semidirect |
| 103. M32 | C3×D9 | semidirect |
| 105. C3×C9 | #361 | semidirect |
| 152. C9 | C3×#361 | semidirect |
| 174. C3 | #10588193 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D72 | 2 |
| C3×C9×M32 | 2 |
| C3×#63372 | 2 |
| C3×#4516 | 3 |
| #10588193 | 3 |