Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
164 conjugacy classes of subgroups; only the 42 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 42 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. #10590023 | C3 | direct (N × H) |
| 62. C33 | #364 | semidirect |
| 91. C32 | C3×#364 | semidirect |
| 108. C3 | #10590023 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×C8×#157 | 2 |
| C3×#63544 | 2 |
| #10590023 | 3 |
| C3×#364 | 9 |