Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
318 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 318 conjugacy classes of subgroups — too many to draw. Only its 80 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. C3×#3799 | C2 | semidirect |
| 2. C3×#3795 | C2 | semidirect |
| 3. C3×#3744 | C2 | semidirect |
| 4. C32×#204 | C2 | semidirect |
| 5. C32×D3×C8 | C2 | semidirect |
| 6. C3×#3719 | C2 | semidirect |
| 7. C3×#3714 | C2 | semidirect |
| 10. #63806 | C3 | direct (N × H) |
| 26. #3799 | C2×C3 | semidirect |
| 27. #3795 | C2×C3 | semidirect |
| 30. #3744 | C2×C3 | semidirect |
| 39. C3×#204 | D3 | semidirect |
| 40. C3×#204 | C2×C3 | semidirect |
| 42. C3×D3×C8 | D3 | semidirect |
| 43. C3×D3×C8 | C2×C3 | semidirect |
| 44. #3719 | C2×C3 | semidirect |
| 45. #3714 | C2×C3 | semidirect |
| 125. #204 | C3×D3 | semidirect |
| 126. D3×C8 | C3×D3 | semidirect |
| 159. C33 | #135 | semidirect |
| 264. C32 | #904 | semidirect |
| 265. C32 | #916 | semidirect |
| 266. C32 | C3×#135 | semidirect |
| 308. C3 | #63806 | direct (N × H) |
| 309. C3 | C3×#904 | semidirect |
| 310. C3 | C3×#916 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#3799 | 2 |
| C3×#3795 | 2 |
| C3×#3744 | 2 |
| C32×#204 | 2 |
| C32×D3×C8 | 2 |
| C3×#3719 | 2 |
| C3×#3714 | 2 |
| C3×#916 | 3 |
| C3×#904 | 3 |
| #63806 | 3 |