Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
264 conjugacy classes of subgroups; only the 40 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 40 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. #10590199 | C3 | direct (N × H) |
| 95. C33 | #362 | semidirect |
| 139. C32 | C3×#362 | semidirect |
| 160. C3 | #10590199 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×Q16×C3⋊D3 | 2 |
| C3×#63770 | 2 |
| C3×#63765 | 2 |
| #10590199 | 3 |
| C3×#362 | 9 |