Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
206 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 206 conjugacy classes of subgroups — too many to draw. Only its 59 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. #88534 | C2 | semidirect |
| 3. C3×C4⋊Dic9 | C2 | semidirect |
| 6. Dic9⋊Dic3 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 27. C4⋊Dic9 | D3 | semidirect |
| 105. C3×C9 | #126 | semidirect |
| 167. C9 | #898 | semidirect |
| 197. C3 | #63441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88534 | 2 |
| C9×(C2×D3)⋊C4 | 2 |
| C3×C4⋊Dic9 | 2 |
| (C2×D3)⋊Dic9 | 2 |
| Dic9⋊Dic3 | 2 |
| Dic3×Dic9 | 2 |
| #63858 | 3 |
| #63441 | 3 |