Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
248 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 77 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×Dic18 | C2 | semidirect |
| 3. C4⋊(C3⋊Dic9) | C2 | semidirect |
| 5. #88442 | C2 | semidirect |
| 21. C2×Dic18 | D3 | semidirect |
| 29. C2×D3×C9 | Q8 | semidirect |
| 87. C3×C9 | C22⋊Q8 | semidirect |
| 128. C2×D3 | Dic18 | semidirect |
| 141. C9 | #946 | semidirect |
| 169. C3 | #63486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×D3×C9 | 2 |
| C2×C3×Dic18 | 2 |
| C4⋊(C3⋊Dic9) | 2 |
| (C2×D3)⋊Dic9 | 2 |
| #88442 | 2 |
| #63856 | 3 |
| #63486 | 3 |