Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
264 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 264 conjugacy classes of subgroups — too many to draw. Only its 70 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. #63481⋊C3 | C2 | semidirect |
| 2. 3−1+2×Q32 | C2 | semidirect |
| 3. #63387⋊C3 | C2 | semidirect |
| 4. D144⋊C3 | C2 | semidirect |
| 5. C16×AGL(1,ℤ/9) | C2 | semidirect |
| 7. #10588599 | C3 | semidirect |
| 20. #63481 | C2×C3 | semidirect |
| 22. C9×Q32 | C2×C3 | semidirect |
| 23. #63387 | C2×C3 | semidirect |
| 24. D144 | C2×C3 | semidirect |
| 25. C16×D9 | C2×C3 | semidirect |
| 113. Q32 | AGL(1,ℤ/9) | semidirect |
| 117. 3−1+2 | #508 | semidirect |
| 158. C9 | C3×#508 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63481⋊C3 | 2 |
| 3−1+2×Q32 | 2 |
| #63387⋊C3 | 2 |
| D144⋊C3 | 2 |
| C16×AGL(1,ℤ/9) | 2 |
| C3×#4919 | 3 |
| #10588599 | 3 |