Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 61 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 61 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 |
| 3. C9×#217 | C2 | semidirect |
| 4. C3×#3676 | C2 | semidirect |
| 5. #88445 | C2 | semidirect |
| 6. #88445 | C2 | semidirect |
| 7. Dic3×Dic9 | C2 | semidirect |
| 30. #3676 | D3 | semidirect |
| 83. #217 | D9 | semidirect |
| 123. C3×C9 | #124 | semidirect |
| 202. C9 | #885 | semidirect |
| 240. C3 | #63447 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#6233 | 2 |
| C2×#6189 | 2 |
| C9×#217 | 2 |
| C3×#3676 | 2 |
| #88445 | 2 |
| Dic3×Dic9 | 2 |
| #63953 | 3 |
| #63447 | 3 |