Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
420 conjugacy classes of subgroups; only the 116 normal subgroups are shown.
This group has 420 conjugacy classes of subgroups — too many to draw. Only its 116 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. #63455⋊C3 | C2 | semidirect |
| 3. 3−1+2×#107 | C2 | semidirect |
| 4. C8×3−1+2⋊C4 | C2 | semidirect |
| 5. #63369⋊C3 | C2 | semidirect |
| 7. #10588552 | C3 | semidirect |
| 15. D72⋊C3 | C4 | semidirect |
| 22. #63455 | C2×C3 | semidirect |
| 24. C9×#107 | C2×C3 | semidirect |
| 25. C8×Dic9 | C2×C3 | semidirect |
| 26. #63369 | C2×C3 | semidirect |
| 33. C4⋊AGL(1,ℤ/9) | C2×C4 | semidirect |
| 35. C8×3−1+2 | C2×C4 | semidirect |
| 56. D72 | C3×C4 | semidirect |
| 65. 3−1+2⋊C4 | D8 | semidirect |
| 94. D36 | C2×C3×C4 | semidirect |
| 97. C8×C9 | C2×C3×C4 | semidirect |
| 141. Dic9 | C3×D8 | semidirect |
| 144. #107 | AGL(1,ℤ/9) | semidirect |
| 147. 3−1+2 | C4×D8 | semidirect |
| 207. C9 | C3×C4×D8 | semidirect |
| 217. 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×D72⋊C3 | 2 |
| #63455⋊C3 | 2 |
| 3−1+2×#107 | 2 |
| C8×3−1+2⋊C4 | 2 |
| #63369⋊C3 | 2 |
| C3×#4872 | 3 |
| #10588552 | 3 |