Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
486 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 104 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. C22×C3×C3⋊Dic3 | C2 | semidirect |
| 3. C32×#217 | C2 | semidirect |
| 4. C3×Dic3⋊Dic3 | C2 | semidirect |
| 5. C3×(C2×D3)⋊Dic3 | C2 | semidirect |
| 8. #63962 | C3 | direct (N × H) |
| 17. C22×C3⋊Dic3 | C2×C3 | semidirect |
| 27. C3×#217 | D3 | semidirect |
| 28. C3×#217 | C2×C3 | semidirect |
| 32. Dic3⋊Dic3 | C2×C3 | semidirect |
| 33. (C2×D3)⋊Dic3 | C2×C3 | semidirect |
| 94. #217 | C3×D3 | semidirect |
| 140. C33 | #123 | semidirect |
| 247. C32 | #886 | semidirect |
| 248. C32 | #935 | semidirect |
| 249. C32 | C3×#123 | semidirect |
| 294. C3 | #63962 | direct (N × H) |
| 295. C3 | C3×#886 | semidirect |
| 296. C3 | C3×#935 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C3⋊Dic3 | 2 |
| C2×C32×#67 | 2 |
| C32×#217 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×(C2×D3)⋊Dic3 | 2 |
| C3×#935 | 3 |
| C3×#886 | 3 |
| #63962 | 3 |