Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
208 conjugacy classes of subgroups; only the 75 normal subgroups are shown.
This group has 208 conjugacy classes of subgroups — too many to draw. Only its 75 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⋊(C9⋊C8) | C2 | semidirect |
| 3. C9×#208 | C2 | semidirect |
| 4. #88413 | C2 | semidirect |
| 5. D9×C3⋊C8 | C2 | semidirect |
| 60. #208 | D9 | semidirect |
| 81. C3×C9 | #131 | semidirect |
| 129. C9 | #948 | semidirect |
| 152. C3 | #63469 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3697 | 2 |
| C2×C3⋊(C9⋊C8) | 2 |
| C9×#208 | 2 |
| #88413 | 2 |
| D9×C3⋊C8 | 2 |
| #63815 | 3 |
| #63469 | 3 |