Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3780 conjugacy classes of subgroups; only the 891 normal subgroups are shown.
This group has 3780 conjugacy classes of subgroups — too many to draw. Only its 891 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. C22×#6308 | C2 | semidirect |
| 3. C33×#117 | C2 | semidirect |
| 4. #11723938 | C2 | semidirect |
| 5. #11723927 | C2 | semidirect |
| 6. #11723916 | C2 | semidirect |
| 7. #11723910 | C2 | semidirect |
| 26. C32×#117 | D3 | semidirect |
| 74. C3×#117 | C3⋊D3 | semidirect |
| 130. #117 | C3⋊(C3⋊D3) | semidirect |
| 131. C33 | #536 | semidirect |
| 176. C32 | #5526 | semidirect |
| 206. C3 | #10595997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89076 | 2 |
| C22×#6308 | 2 |
| C33×#117 | 2 |
| #11723938 | 2 |
| #11723927 | 2 |
| #11723916 | 2 |
| #11723910 | 2 |
| #10595997 | 3 |