Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
211 conjugacy classes of subgroups; only the 51 normal subgroups are shown.
This group has 211 conjugacy classes of subgroups — too many to draw. Only its 51 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×C9×SL(2,𝔽3) | C2 | semidirect |
| 3. D3×Q8×C9 | C3 | semidirect |
| 5. D3×Q8⋊C9 | C3 | semidirect |
| 8. C3×Q8×C9 | C2×C3 | semidirect |
| 11. C3×Q8⋊C9 | C2×C3 | semidirect |
| 15. C9×SL(2,𝔽3) | D3 | direct (N × H) |
| 20. D3×SL(2,𝔽3) | C9 | direct (N × H) |
| 35. C3×SL(2,𝔽3) | C2×C9 | semidirect |
| 39. Q8×C9 | C3×D3 | semidirect |
| 42. Q8⋊C9 | C3×D3 | semidirect |
| 53. D3×C9 | SL(2,𝔽3) | direct (N × H) |
| 55. D3×Q8 | C3×C9 | semidirect |
| 73. C3×C9 | C2×SL(2,𝔽3) | semidirect |
| 76. C3×Q8 | C2×C3×C9 | semidirect |
| 82. SL(2,𝔽3) | D3×C9 | direct (N × H) |
| 114. C9 | D3×SL(2,𝔽3) | direct (N × H) |
| 116. Q8 | C3×D3×C9 | semidirect |
| 125. D3 | C9×SL(2,𝔽3) | direct (N × H) |
| 132. C3 | C2×C9×SL(2,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C9×SL(2,𝔽3) | 2 |
| C3×D3×SL(2,𝔽3) | 3 |
| D3×Q8×C9 | 3 |
| C2×C9×SL(2,𝔽3) | 3 |
| D3×Q8⋊C9 | 3 |
| C2×C3×D3×C9 | 4 |