Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
300 conjugacy classes of subgroups; only the 77 normal subgroups are shown.
This group has 300 conjugacy classes of subgroups — too many to draw. Only its 77 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 |
|---|---|---|
| 4. C32×#216 | C3 | semidirect |
| 28. C3×H(3,𝔽3) | Q16 | semidirect |
| 45. #216 | H(3,𝔽3) | direct (N × H) |
| 59. C33 | C3×Q16 | semidirect |
| 61. H(3,𝔽3) | #216 | direct (N × H) |
| 95. C32 | C3×#216 | semidirect |
| 111. C3 | Q16×H(3,𝔽3) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q8×H(3,𝔽3) | 2 |
| Dic6×H(3,𝔽3) | 2 |
| C3⋊C8×H(3,𝔽3) | 2 |
| C32×#216 | 3 |
| Q16×H(3,𝔽3) | 3 |