Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
218 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 218 conjugacy classes of subgroups — too many to draw. Only its 55 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 |
| 27. C22×C33 | C16 | semidirect |
| 68. C22×C32 | C3⋊C16 | semidirect |
| 78. C33 | C22⋊C16 | semidirect |
| 119. C22×C3 | #3771 | semidirect |
| 129. C32 | #4549 | semidirect |
| 151. C22 | C3⋊#3771 | semidirect |
| 158. C3 | C22⋊#3771 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#622 | 2 |
| C2×C3⋊#3771 | 2 |
| C22⋊#3771 | 3 |
| #4549 | 9 |