Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
362 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 362 conjugacy classes of subgroups — too many to draw. Only its 86 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 |
|---|---|---|
| 1. C2×D8×3−1+2 | C2 | semidirect |
| 2. #63495⋊C3 | C2 | semidirect |
| 3. #63464⋊C3 | C2 | semidirect |
| 4. #63391⋊C3 | C2 | semidirect |
| 5. #63372⋊C3 | C2 | semidirect |
| 7. #10588840 | C3 | semidirect |
| 25. C2×C9×D8 | C2×C3 | semidirect |
| 26. #63495 | C2×C3 | semidirect |
| 27. #63464 | C2×C3 | semidirect |
| 28. #63391 | C2×C3 | semidirect |
| 29. #63372 | C2×C3 | semidirect |
| 164. C2×D8 | AGL(1,ℤ/9) | semidirect |
| 168. 3−1+2 | #472 | semidirect |
| 231. C9 | C3×#472 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D8×3−1+2 | 2 |
| #63495⋊C3 | 2 |
| #63464⋊C3 | 2 |
| #63391⋊C3 | 2 |
| #63372⋊C3 | 2 |
| C3×#5160 | 3 |
| #10588840 | 3 |