Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
422 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 96 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×D3×Dic3 | C2 | semidirect |
| 3. C3×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 4. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 5. C32×(C2×D3)⋊C4 | C2 | semidirect |
| 6. C3×Dic3⋊Dic3 | C2 | semidirect |
| 7. C3×(C2×D3)⋊Dic3 | C2 | semidirect |
| 10. #63891 | C3 | direct (N × H) |
| 25. C2×D3×Dic3 | C2×C3 | semidirect |
| 28. C4⋊(C3⋊Dic3) | C2×C3 | semidirect |
| 33. C3×(C2×D3)⋊C4 | D3 | semidirect |
| 34. C3×(C2×D3)⋊C4 | D3 | semidirect |
| 35. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 36. C3×(C2×D3)⋊C4 | C2×C3 | semidirect |
| 42. Dic3⋊Dic3 | C2×C3 | semidirect |
| 43. (C2×D3)⋊Dic3 | C2×C3 | semidirect |
| 118. (C2×D3)⋊C4 | C3×D3 | semidirect |
| 119. (C2×D3)⋊C4 | C3×D3 | semidirect |
| 180. C33 | #123 | semidirect |
| 312. C32 | #883 | semidirect |
| 313. C32 | #886 | semidirect |
| 314. C32 | C3×#123 | semidirect |
| 369. C3 | #63891 | direct (N × H) |
| 370. C3 | C3×#883 | semidirect |
| 371. C3 | C3×#886 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#625 | 2 |
| C2×C3×D3×Dic3 | 2 |
| C3×C4⋊(C3⋊Dic3) | 2 |
| C32×(C2×D3)⋊C4 | 2 |
| C3×Dic3⋊Dic3 | 2 |
| C3×(C2×D3)⋊Dic3 | 2 |
| C3×#886 | 3 |
| C3×#883 | 3 |
| #63891 | 3 |