Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
206 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 76 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×C9×C4⋊C4 | C2 | semidirect |
| 5. C3×C4⋊Dic9 | C2 | semidirect |
| 6. C3×Dic9⋊C4 | C2 | semidirect |
| 7. C3×C4×Dic9 | C2 | semidirect |
| 9. #63460 | C3 | direct (N × H) |
| 25. C9×C4⋊C4 | C2×C3 | semidirect |
| 29. C4⋊Dic9 | C2×C3 | semidirect |
| 30. Dic9⋊C4 | C2×C3 | semidirect |
| 31. C4×Dic9 | C2×C3 | semidirect |
| 68. C3×C4⋊C4 | D9 | semidirect |
| 105. C3×C9 | #126 | semidirect |
| 136. C4⋊C4 | C3×D9 | semidirect |
| 167. C9 | C3×#126 | semidirect |
| 197. C3 | #63460 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×C4⋊C4 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×C4⋊Dic9 | 2 |
| C3×Dic9⋊C4 | 2 |
| C3×C4×Dic9 | 2 |
| C3×#898 | 3 |
| #63460 | 3 |