Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
446 conjugacy classes of subgroups; only the 176 normal subgroups are shown.
This group has 446 conjugacy classes of subgroups — too many to draw. Only its 176 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 |
|---|---|---|
| 3. 3−1+2×#97 | C2 | semidirect |
| 4. C8×3−1+2⋊C4 | C2 | semidirect |
| 5. #63362⋊C3 | C2 | semidirect |
| 7. #10588388 | C3 | semidirect |
| 15. #3663⋊C3 | C4 | semidirect |
| 24. C9×#97 | C2×C3 | semidirect |
| 25. C8×Dic9 | C2×C3 | semidirect |
| 26. #63362 | C2×C3 | semidirect |
| 34. C8×3−1+2 | C2×C4 | semidirect |
| 35. 3−1+2⋊C8 | C2×C4 | semidirect |
| 55. #3663 | C3×C4 | semidirect |
| 62. 3−1+2⋊C4 | M16 | semidirect |
| 92. C8×C9 | C2×C3×C4 | semidirect |
| 93. C9⋊C8 | C2×C3×C4 | semidirect |
| 130. Dic9 | C3×M16 | semidirect |
| 134. #97 | AGL(1,ℤ/9) | semidirect |
| 136. 3−1+2 | C4×M16 | semidirect |
| 187. C9 | C3×C4×M16 | semidirect |
| 196. C8 | C4×AGL(1,ℤ/9) | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3663⋊C3 | 2 |
| C42×AGL(1,ℤ/9) | 2 |
| 3−1+2×#97 | 2 |
| C8×3−1+2⋊C4 | 2 |
| #63362⋊C3 | 2 |
| C3×#4707 | 3 |
| #10588388 | 3 |