Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
343 conjugacy classes of subgroups; only the 86 normal subgroups are shown.
This group has 343 conjugacy classes of subgroups — too many to draw. Only its 86 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. #63454⋊C3 | C2 | semidirect |
| 3. 3−1+2×#102 | C2 | semidirect |
| 4. #63392⋊C3 | C2 | semidirect |
| 5. (C2×AGL(1,ℤ/9))⋊C8 | C2 | semidirect |
| 6. #63378⋊C3 | C2 | semidirect |
| 7. #63367⋊C3 | C2 | semidirect |
| 9. #10588464 | C3 | semidirect |
| 29. #63454 | C2×C3 | semidirect |
| 31. C9×#102 | C2×C3 | semidirect |
| 32. #63392 | C2×C3 | semidirect |
| 33. (C2×D9)⋊C8 | C2×C3 | semidirect |
| 34. #63378 | C2×C3 | semidirect |
| 35. #63367 | C2×C3 | semidirect |
| 204. #102 | AGL(1,ℤ/9) | semidirect |
| 206. 3−1+2 | #482 | semidirect |
| 288. C9 | C3×#482 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63500⋊C3 | 2 |
| #63454⋊C3 | 2 |
| 3−1+2×#102 | 2 |
| #63392⋊C3 | 2 |
| (C2×AGL(1,ℤ/9))⋊C8 | 2 |
| #63378⋊C3 | 2 |
| #63367⋊C3 | 2 |
| C3×#4784 | 3 |
| #10588464 | 3 |