Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
256 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 256 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×#6189 | C2 | semidirect |
| 5. Dic3⋊Dic9 | C2 | semidirect |
| 6. #88442 | C2 | semidirect |
| 7. Dic9⋊Dic3 | C2 | semidirect |
| 36. C22×C3×C9 | Q8 | semidirect |
| 102. C22×C9 | Dic6 | semidirect |
| 113. C3×C9 | C22⋊Q8 | semidirect |
| 162. C22×C3 | Dic18 | semidirect |
| 182. C9 | #878 | semidirect |
| 206. C22 | #6189 | semidirect |
| 215. C3 | #63486 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×Dic3 | 2 |
| C2×#6189 | 2 |
| #88551 | 2 |
| C3×#3676 | 2 |
| Dic3⋊Dic9 | 2 |
| #88442 | 2 |
| Dic9⋊Dic3 | 2 |
| #63964 | 3 |
| #63486 | 3 |