Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
634 conjugacy classes of subgroups; only the 182 normal subgroups are shown.
This group has 634 conjugacy classes of subgroups — too many to draw. Only its 182 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×C3×C4⋊Dic9 | C2 | semidirect |
| 3. C3×C9×#95 | C2 | semidirect |
| 5. #10588357 | C3 | direct (N × H) |
| 15. C2×C4⋊Dic9 | C2×C3 | semidirect |
| 17. C9×#95 | C2×C3 | semidirect |
| 52. C3×#95 | D9 | semidirect |
| 111. #95 | C3×D9 | semidirect |
| 112. C3×C9 | #399 | semidirect |
| 170. C9 | C3×#399 | semidirect |
| 199. C3 | #10588357 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×(C2×D9)⋊C4 | 2 |
| C2×C3×C4⋊Dic9 | 2 |
| C3×C9×#95 | 2 |
| C3×#4677 | 3 |
| #10588357 | 3 |