Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
530 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 530 conjugacy classes of subgroups — too many to draw. Only its 81 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 |
| 3. Dic6×H(3,𝔽3) | C2 | semidirect |
| 4. #10619894 | C2 | semidirect |
| 15. C32×Dic6 | D3 | semidirect |
| 25. C3×#272 | Q8 | semidirect |
| 41. C3×H(3,𝔽3) | C2×Q8 | semidirect |
| 63. #272 | Dic6 | direct (N × H) |
| 87. C33 | D3×Q8 | semidirect |
| 89. H(3,𝔽3) | C2×Dic6 | semidirect |
| 106. Dic6 | #272 | direct (N × H) |
| 140. C32 | D3×Dic6 | semidirect |
| 164. C3 | Q8×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10619988 | 2 |
| C3×C4×#272 | 2 |
| Dic6×H(3,𝔽3) | 2 |
| #10619894 | 2 |
| Dic3×#272 | 2 |
| C3×D3×Dic6 | 3 |
| Q8×#272 | 3 |