Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
256 conjugacy classes of subgroups; only the 65 normal subgroups are shown.
This group has 256 conjugacy classes of subgroups — too many to draw. Only its 65 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 |
|---|---|---|
| 1. C2×C3×Dic18 | C2 | semidirect |
| 4. C9×Dic3⋊C4 | C2 | semidirect |
| 6. #88442 | C2 | semidirect |
| 7. Dic9⋊Dic3 | C2 | semidirect |
| 27. C2×Dic18 | D3 | semidirect |
| 37. C2×C3⋊D9 | Q8 | semidirect |
| 85. Dic3⋊C4 | D9 | semidirect |
| 113. C3×C9 | C22⋊Q8 | semidirect |
| 182. C9 | #946 | semidirect |
| 215. C3 | #63458 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Dic18 | 2 |
| C2×(C3⋊D9)⋊C4 | 2 |
| #88536 | 2 |
| C9×Dic3⋊C4 | 2 |
| #88445 | 2 |
| #88442 | 2 |
| Dic9⋊Dic3 | 2 |
| #63888 | 3 |
| #63458 | 3 |