Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
268 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 66 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. C3×#63394 | C2 | semidirect |
| 4. #10588219 | C3 | direct (N × H) |
| 14. #63394 | C2×C3 | semidirect |
| 107. C3×C9 | #355 | semidirect |
| 162. C9 | C3×#355 | semidirect |
| 186. C3 | #10588219 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×#124 | 2 |
| C3×#63394 | 2 |
| C3×#4542 | 3 |
| #10588219 | 3 |