Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
656 conjugacy classes of subgroups; only the 198 normal subgroups are shown.
This group has 656 conjugacy classes of subgroups — too many to draw. Only its 198 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 |
|---|---|---|
| 3. #10589412 | C3 | direct (N × H) |
| 87. C33 | #333 | semidirect |
| 128. C32 | #4546 | semidirect |
| 129. C32 | C3×#333 | semidirect |
| 147. C3 | C3×#4546 | semidirect |
| 148. C3 | #10589412 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C33×C4⋊Q8 | 2 |
| C3×C4⋊(C3⋊(C3⋊C8)) | 2 |
| #10589412 | 3 |
| C3×#4546 | 3 |