Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
260 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 260 conjugacy classes of subgroups — too many to draw. Only its 80 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×D9 | C2 | semidirect |
| 3. C3×C9×C4⋊C4 | C2 | semidirect |
| 4. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 5. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 6. C3×(C2×D9)⋊C4 | C2 | semidirect |
| 7. C3×Dic9⋊C4 | C2 | semidirect |
| 9. #63456 | C3 | direct (N × H) |
| 27. C2×C4×D9 | C2×C3 | semidirect |
| 29. C9×C4⋊C4 | C2×C3 | semidirect |
| 30. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 31. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 32. (C2×D9)⋊C4 | C2×C3 | semidirect |
| 33. Dic9⋊C4 | C2×C3 | semidirect |
| 80. C3×C4⋊C4 | D9 | semidirect |
| 118. C3×C9 | #123 | semidirect |
| 156. C4⋊C4 | C3×D9 | semidirect |
| 190. C9 | C3×#123 | semidirect |
| 226. C3 | #63456 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D36 | 2 |
| C2×C3×C4×D9 | 2 |
| C3×C9×C4⋊C4 | 2 |
| C3×(C2×D9)⋊C4 | 2 |
| C3×Dic9⋊C4 | 2 |
| C3×#894 | 3 |
| #63456 | 3 |