Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
2212 conjugacy classes of subgroups; only the 419 normal subgroups are shown.
This group has 2212 conjugacy classes of subgroups — too many to draw. Only its 419 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. C2×C8×C3⋊(C3⋊D3) | C2 | semidirect |
| 3. #11723933 | C2 | semidirect |
| 4. C33×#102 | C2 | semidirect |
| 5. #11722202 | C2 | semidirect |
| 6. #11722186 | C2 | semidirect |
| 7. #11722180 | C2 | semidirect |
| 13. #89078 | C4 | semidirect |
| 26. C32×#102 | D3 | semidirect |
| 78. C3×#102 | C3⋊D3 | semidirect |
| 138. #102 | C3⋊(C3⋊D3) | semidirect |
| 139. C33 | #416 | semidirect |
| 189. C32 | #4772 | semidirect |
| 225. C3 | #10592471 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#89078 | 2 |
| C2×C8×C3⋊(C3⋊D3) | 2 |
| #11723933 | 2 |
| C33×#102 | 2 |
| #11722202 | 2 |
| #11722186 | 2 |
| #11722180 | 2 |
| #10592471 | 3 |