Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
218 conjugacy classes of subgroups; only the 44 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 44 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 |
|---|---|---|
| 2. C2×C3⋊#3771 | C2 | semidirect |
| 3. C2×C3×#3771 | C2 | semidirect |
| 14. C2×#3771 | D3 | semidirect |
| 35. C2×C3⋊(C3⋊D3) | C16 | semidirect |
| 90. C33 | C22⋊C16 | semidirect |
| 144. C32 | (C2×D3)⋊C16 | semidirect |
| 174. C3 | #10593264 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88924 | 2 |
| C2×C3⋊#3771 | 2 |
| C2×C3×#3771 | 2 |
| #10593264 | 3 |
| (C2×D3)⋊C16 | 9 |