Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
608 conjugacy classes of subgroups; only the 172 normal subgroups are shown.
This group has 608 conjugacy classes of subgroups — too many to draw. Only its 172 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. #11722182 | C2 | semidirect |
| 3. C2×C32×C3⋊C16 | C2 | semidirect |
| 4. #11722002 | C2 | semidirect |
| 5. C3⋊D3×C3⋊C16 | C2 | semidirect |
| 24. C2×C3×C3⋊C16 | D3 | semidirect |
| 68. C2×C3⋊C16 | C3⋊D3 | semidirect |
| 130. C33 | #504 | semidirect |
| 180. C32 | #4901 | semidirect |
| 181. C32 | #5140 | semidirect |
| 204. C3 | #10590621 | semidirect |
| 205. C3 | #10592600 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#64110 | 2 |
| #11722182 | 2 |
| C2×C32×C3⋊C16 | 2 |
| #11722002 | 2 |
| C3⋊D3×C3⋊C16 | 2 |
| #10592600 | 3 |
| #10590621 | 3 |