Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
282 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 282 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×C3×Dic18 | C2 | semidirect |
| 3. C4×C9×Dic3 | C2 | semidirect |
| 4. #88445 | C2 | semidirect |
| 19. C2×Dic18 | D3 | semidirect |
| 56. C4×Dic3 | D9 | semidirect |
| 74. C3×C9 | #124 | semidirect |
| 121. C9 | #947 | semidirect |
| 144. C3 | #63437 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4⋊(C3⋊D9) | 2 |
| C2×C3×Dic18 | 2 |
| C4×C9×Dic3 | 2 |
| #88445 | 2 |
| #63864 | 3 |
| #63437 | 3 |