Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
304 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 304 conjugacy classes of subgroups — too many to draw. Only its 49 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 |
|---|---|---|
| 1. C3×#63700 | C2 | semidirect |
| 2. C3⋊#63700 | C2 | semidirect |
| 3. C3⋊(#131⋊C9) | C2 | semidirect |
| 19. #63700 | D3 | semidirect |
| 26. #5835 | C9 | semidirect |
| 281. C3 | #576⋊C9 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63700 | 2 |
| C3⋊#63700 | 2 |
| C3⋊(#131⋊C9) | 2 |
| C3×#5835 | 3 |
| #576⋊C9 | 3 |
| C9×#216 | 4 |