Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
338 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 338 conjugacy classes of subgroups — too many to draw. Only its 75 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×#88428 | C2 | semidirect |
| 5. #11720556 | C2 | semidirect |
| 6. C3×#63381 | C2 | semidirect |
| 7. #11720299 | C2 | semidirect |
| 39. #63381 | D3 | semidirect |
| 213. C3×C9 | #473 | semidirect |
| 295. C9 | #4896 | semidirect |
| 328. C3 | #10588882 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C9×#909 | 2 |
| C2×#88428 | 2 |
| #11720891 | 2 |
| #11720877 | 2 |
| #11720556 | 2 |
| C3×#63381 | 2 |
| #11720299 | 2 |
| #10590983 | 3 |
| #10588882 | 3 |