Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
230 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 230 conjugacy classes of subgroups — too many to draw. Only its 67 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×#634⋊C3 | C2 | semidirect |
| 3. M16×H(3,𝔽3) | C2 | semidirect |
| 4. #3744⋊C3 | C2 | semidirect |
| 5. #3746⋊C3 | C2 | semidirect |
| 6. #64118 | C3 | semidirect |
| 18. C2×#634 | C2×C3 | semidirect |
| 22. C32×M16 | D3 | semidirect |
| 23. C32×M16 | C2×C3 | semidirect |
| 24. #3746 | C2×C3 | semidirect |
| 25. #3744 | C2×C3 | semidirect |
| 92. H(3,𝔽3) | #137 | semidirect |
| 134. M16 | (C3⋊D3)⋊C3 | semidirect |
| 157. C32 | #909 | semidirect |
| 158. C32 | C3×#137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3828⋊C3 | 2 |
| C2×#634⋊C3 | 2 |
| M16×H(3,𝔽3) | 2 |
| #3744⋊C3 | 2 |
| #3746⋊C3 | 2 |
| #64118 | 3 |
| C3×#909 | 3 |