Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
214 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 214 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 |
|---|---|---|
| 4. Dic3⋊Dic9 | C2 | semidirect |
| 5. #88442 | C2 | semidirect |
| 6. Dic9⋊Dic3 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 107. C3×C9 | #126 | semidirect |
| 172. C9 | #879 | semidirect |
| 203. C3 | #63441 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #88551 | 2 |
| C9×#217 | 2 |
| C3×#3676 | 2 |
| Dic3⋊Dic9 | 2 |
| #88442 | 2 |
| Dic9⋊Dic3 | 2 |
| Dic3×Dic9 | 2 |
| #63956 | 3 |
| #63441 | 3 |