Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 136 normal subgroups are shown.
This group has 282 conjugacy classes of subgroups — too many to draw. Only its 136 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 |
|---|---|---|
| 3. C3×C4⋊Dic9 | C2 | semidirect |
| 4. C3×C4×Dic9 | C2 | semidirect |
| 6. #63488 | C3 | direct (N × H) |
| 8. C2×C3×C4×C9 | C4 | semidirect |
| 19. C4⋊Dic9 | C2×C3 | semidirect |
| 20. C4×Dic9 | C2×C3 | semidirect |
| 39. C2×C4×C9 | C3×C4 | semidirect |
| 73. C3×C9 | #117 | semidirect |
| 81. C2×C3×C4 | Dic9 | semidirect |
| 120. C9 | C3×#117 | semidirect |
| 123. C2×C4 | C3×Dic9 | semidirect |
| 142. C3 | #63488 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C4×C9 | 2 |
| C3×#3676 | 2 |
| C3×C4⋊Dic9 | 2 |
| C3×C4×Dic9 | 2 |
| C3×#926 | 3 |
| #63488 | 3 |