Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
268 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 268 conjugacy classes of subgroups — too many to draw. Only its 71 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. C22×C9×Dic3 | C2 | semidirect |
| 3. #88551 | C2 | semidirect |
| 4. (C2×D9)⋊Dic3 | C2 | semidirect |
| 5. #88442 | C2 | semidirect |
| 59. C22×Dic3 | D9 | semidirect |
| 88. C3×C9 | #123 | semidirect |
| 143. C9 | #935 | semidirect |
| 171. C3 | #63491 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#611 | 2 |
| C22×C9×Dic3 | 2 |
| #88551 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| #88442 | 2 |
| #63961 | 3 |
| #63491 | 3 |