Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
212 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 212 conjugacy classes of subgroups — too many to draw. Only its 67 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. #11720534 | C2 | semidirect |
| 3. C3×#63372 | C2 | semidirect |
| 16. #63372 | D3 | semidirect |
| 105. C3×C9 | #361 | semidirect |
| 152. C9 | #4495 | semidirect |
| 174. C3 | #10588240 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×D24 | 2 |
| #11720534 | 2 |
| C3×#63372 | 2 |
| #10589126 | 3 |
| #10588240 | 3 |