Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
202 conjugacy classes of subgroups; only the 35 normal subgroups are shown.
This group has 202 conjugacy classes of subgroups — too many to draw. Only its 35 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. #11724237 | C2 | semidirect |
| 3. C3×#63746 | C2 | semidirect |
| 9. #88941 | C4 | semidirect |
| 13. #63746 | D3 | semidirect |
| 83. C33 | #357 | semidirect |
| 132. C32 | #4491 | semidirect |
| 160. C3 | #10593160 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11724336 | 2 |
| #11724237 | 2 |
| C3×#63746 | 2 |
| #10593160 | 3 |
| #4491 | 9 |