Finite Group DatabasebetaFinite Group DatabasebetaOrder 864.
142 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 142 conjugacy classes of subgroups — too many to draw. Only its 35 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⋊AGL(1,𝔽9) | C2 | semidirect |
| 11. C22×C33 | C8 | semidirect |
| 14. C2×C3×C3⋊D3 | C8 | semidirect |
| 34. C22×C32 | C3⋊C8 | semidirect |
| 37. C2×C3⋊D3 | C3⋊C8 | semidirect |
| 46. C33 | C22⋊C8 | semidirect |
| 73. C22×C3 | AGL(1,𝔽9) | semidirect |
| 82. C32 | #830 | semidirect |
| 104. C22 | C3⋊AGL(1,𝔽9) | semidirect |
| 109. C3 | C22⋊AGL(1,𝔽9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#157 | 2 |
| C2×C3⋊AGL(1,𝔽9) | 2 |
| C22⋊AGL(1,𝔽9) | 3 |
| #830 | 9 |