Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
481 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 481 conjugacy classes of subgroups — too many to draw. Only its 100 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. C2×#3672⋊C3 | C2 | semidirect |
| 3. C2×Dic36⋊C3 | C2 | semidirect |
| 4. #63459⋊C3 | C2 | semidirect |
| 5. 3−1+2×#102 | C2 | semidirect |
| 6. (C2×AGL(1,ℤ/9))⋊C8 | C2 | semidirect |
| 7. #63368⋊C3 | C2 | semidirect |
| 9. #10588463 | C3 | semidirect |
| 33. C2×#3672 | C2×C3 | semidirect |
| 34. C2×Dic36 | C2×C3 | semidirect |
| 35. #63459 | C2×C3 | semidirect |
| 37. C9×#102 | C2×C3 | semidirect |
| 38. (C2×D9)⋊C8 | C2×C3 | semidirect |
| 39. #63368 | C2×C3 | semidirect |
| 239. #102 | AGL(1,ℤ/9) | semidirect |
| 241. 3−1+2 | #452 | semidirect |
| 337. C9 | C3×#452 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#3699⋊C3 | 2 |
| C2×#3672⋊C3 | 2 |
| C2×Dic36⋊C3 | 2 |
| #63459⋊C3 | 2 |
| 3−1+2×#102 | 2 |
| (C2×AGL(1,ℤ/9))⋊C8 | 2 |
| #63368⋊C3 | 2 |
| C3×#4783 | 3 |
| #10588463 | 3 |