Finite Group DatabasebetaFinite Group DatabasebetaOrder 1296.
360 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 360 conjugacy classes of subgroups — too many to draw. Only its 70 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 |
|---|---|---|
| 5. #88550 | C3 | direct (N × H) |
| 28. C3×H(3,𝔽3) | Q16 | semidirect |
| 56. C33 | #216 | semidirect |
| 58. H(3,𝔽3) | C3×Q16 | semidirect |
| 87. C32 | C3×#216 | semidirect |
| 101. C3 | #88550 | direct (N × H) |
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 |
| C3×#6229 | 2 |
| C3×#6180 | 2 |
| C32×#216 | 3 |
| #88550 | 3 |