Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
164 conjugacy classes of subgroups; only the 39 normal subgroups are shown.
This group has 164 conjugacy classes of subgroups — too many to draw. Only its 39 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. #11724238 | C2 | semidirect |
| 3. #11724237 | C2 | semidirect |
| 81. C33 | #350 | semidirect |
| 124. C32 | #4561 | semidirect |
| 147. C3 | #10593271 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64289 | 2 |
| #11724238 | 2 |
| #11724237 | 2 |
| #10593271 | 3 |
| #4561 | 9 |