Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
520 conjugacy classes of subgroups; only the 91 normal subgroups are shown.
This group has 520 conjugacy classes of subgroups — too many to draw. Only its 91 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. #10619988 | C2 | semidirect |
| 2. C3×#6229 | C2 | semidirect |
| 4. #10619894 | C2 | semidirect |
| 23. #6229 | D3 | direct (N × H) |
| 25. D3×H(3,𝔽3) | Q8 | semidirect |
| 41. C3×H(3,𝔽3) | C2×Q8 | semidirect |
| 60. C32×D3 | Dic6 | semidirect |
| 86. C33 | C2×Dic6 | semidirect |
| 88. H(3,𝔽3) | D3×Q8 | semidirect |
| 137. C32 | D3×Dic6 | semidirect |
| 151. D3 | #6229 | direct (N × H) |
| 160. C3 | C2×#6229 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619988 | 2 |
| C3×#6229 | 2 |
| C4×D3×H(3,𝔽3) | 2 |
| #10619894 | 2 |
| D3×#1084 | 2 |
| C3×D3×Dic6 | 3 |
| C2×#6229 | 3 |