Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
258 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 258 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. C2×C9×Dic6 | C2 | semidirect |
| 3. C4×C3⋊Dic9 | C2 | semidirect |
| 4. (C2×D9)⋊Dic3 | C2 | semidirect |
| 50. C2×Dic6 | D9 | semidirect |
| 72. C3×C9 | #124 | semidirect |
| 116. C9 | #936 | semidirect |
| 138. C3 | #63509 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D36 | 2 |
| C2×C9×Dic6 | 2 |
| C4×C3⋊Dic9 | 2 |
| (C2×D9)⋊Dic3 | 2 |
| #63863 | 3 |
| #63509 | 3 |