Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
524 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 108 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. #63502⋊C3 | C2 | semidirect |
| 3. C2×#3673⋊C3 | C2 | semidirect |
| 4. C2×D72⋊C3 | C2 | semidirect |
| 5. C8×3−1+2⋊C4 | C2 | semidirect |
| 7. #10588831 | C3 | semidirect |
| 23. C2×C9×D8 | C2×C3 | semidirect |
| 24. #63502 | C2×C3 | semidirect |
| 25. C2×#3673 | C2×C3 | semidirect |
| 26. C2×D72 | C2×C3 | semidirect |
| 27. C8×Dic9 | C2×C3 | semidirect |
| 37. C8×3−1+2 | D4 | semidirect |
| 38. 3−1+2⋊C8 | D4 | semidirect |
| 69. 3−1+2⋊C4 | D8 | semidirect |
| 105. C8×C9 | C3×D4 | semidirect |
| 106. C9⋊C8 | C3×D4 | semidirect |
| 150. Dic9 | C3×D8 | semidirect |
| 153. C2×D8 | AGL(1,ℤ/9) | semidirect |
| 156. 3−1+2 | #493 | semidirect |
| 217. C9 | C3×#493 | semidirect |
| 228. C8 | #611⋊C3 | 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 |
| #63502⋊C3 | 2 |
| C2×#3673⋊C3 | 2 |
| C2×D72⋊C3 | 2 |
| C8×3−1+2⋊C4 | 2 |
| C3×#5151 | 3 |
| #10588831 | 3 |