Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 79 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 79 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. #88442 | C2 | semidirect |
| 5. Dic3×Dic9 | C2 | semidirect |
| 9. C2×C3⋊Dic9 | C4 | semidirect |
| 84. C3×C9 | #117 | semidirect |
| 136. C9 | #877 | semidirect |
| 160. C3 | #63439 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3⋊Dic9 | 2 |
| C9×#217 | 2 |
| C3×#3676 | 2 |
| #88442 | 2 |
| Dic3×Dic9 | 2 |
| #63957 | 3 |
| #63439 | 3 |