Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
216 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 216 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. #11720535 | C2 | semidirect |
| 3. C3×#63371 | C2 | semidirect |
| 18. #63371 | D3 | semidirect |
| 106. C3×C9 | #361 | semidirect |
| 154. C9 | #4516 | semidirect |
| 176. 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 |
| #11720535 | 2 |
| C3×#63371 | 2 |
| #10589127 | 3 |
| #10588240 | 3 |