Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
367 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 367 conjugacy classes of subgroups — too many to draw. Only its 90 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. C4⋊C4×AGL(1,ℤ/9) | C2 | semidirect |
| 3. 3−1+2×#102 | C2 | semidirect |
| 4. #63392⋊C3 | C2 | semidirect |
| 5. (C2×AGL(1,ℤ/9))⋊C8 | C2 | semidirect |
| 6. #63377⋊C3 | C2 | semidirect |
| 7. #63367⋊C3 | C2 | semidirect |
| 9. #10588457 | C3 | semidirect |
| 29. C4⋊C4×D9 | C2×C3 | semidirect |
| 31. C9×#102 | C2×C3 | semidirect |
| 32. #63392 | C2×C3 | semidirect |
| 33. (C2×D9)⋊C8 | C2×C3 | semidirect |
| 34. #63377 | C2×C3 | semidirect |
| 35. #63367 | C2×C3 | semidirect |
| 207. #102 | AGL(1,ℤ/9) | semidirect |
| 209. 3−1+2 | #481 | semidirect |
| 293. C9 | C3×#481 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #63500⋊C3 | 2 |
| C4⋊C4×AGL(1,ℤ/9) | 2 |
| 3−1+2×#102 | 2 |
| #63392⋊C3 | 2 |
| (C2×AGL(1,ℤ/9))⋊C8 | 2 |
| #63377⋊C3 | 2 |
| #63367⋊C3 | 2 |
| C3×#4777 | 3 |
| #10588457 | 3 |