Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 88 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×Dic18 | C2 | semidirect |
| 3. C3×#3676 | C2 | semidirect |
| 4. C3×C4×Dic9 | C2 | semidirect |
| 6. #63498 | C3 | direct (N × H) |
| 19. C2×Dic18 | C2×C3 | semidirect |
| 20. #3676 | C2×C3 | semidirect |
| 21. C4×Dic9 | C2×C3 | semidirect |
| 74. C3×C9 | #124 | semidirect |
| 121. C9 | C3×#124 | semidirect |
| 144. C3 | #63498 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C9 | 2 |
| C2×C3×Dic18 | 2 |
| C3×#3676 | 2 |
| C3×C4×Dic9 | 2 |
| C3×#936 | 3 |
| #63498 | 3 |