Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
244 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 244 conjugacy classes of subgroups — too many to draw. Only its 40 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×#63692 | C2 | semidirect |
| 2. C3×#131⋊C9 | C2 | semidirect |
| 4. #10589509 | C3 | direct (N × H) |
| 11. #63692 | C2×C3 | semidirect |
| 15. #131⋊C9 | C2×C3 | semidirect |
| 39. C3×#131 | D9 | semidirect |
| 95. #131 | C3×D9 | semidirect |
| 176. C3 | #10589509 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63692 | 2 |
| C3×#131⋊C9 | 2 |
| C3×#5142 | 3 |
| #10589509 | 3 |
| C3×D72 | 4 |