Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
810 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 810 conjugacy classes of subgroups — too many to draw. Only its 254 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 |
|---|---|---|
| 6. #10596193 | C3 | semidirect |
| 36. #634⋊C3 | Q8 | semidirect |
| 100. #634 | C3×Q8 | semidirect |
| 162. H(3,𝔽3) | Q82 | semidirect |
| 230. C32 | #5722 | semidirect |
| 231. C32 | C3×Q82 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| H(3,𝔽3)×C4⋊Q8 | 2 |
| #64153⋊C3 | 2 |
| #64097⋊C3 | 2 |
| #64096⋊C3 | 2 |
| C4×#634⋊C3 | 2 |
| #10596193 | 3 |
| C3×#5722 | 3 |