Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
512 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 126 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 |
|---|---|---|
| 5. C3×#4478 | C3 | direct (N × H) |
| 30. #4478 | C32 | direct (N × H) |
| 121. C33 | #356 | semidirect |
| 175. C32 | #4478 | direct (N × H) |
| 176. C32 | C3×#356 | semidirect |
| 199. C3 | C3×#4478 | direct (N × H) |
| 200. C3 | C32×#356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C32×#944 | 2 |
| C33×#101 | 2 |
| C32×#836 | 2 |
| C32×#356 | 3 |
| C3×#4478 | 3 |