Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
641 conjugacy classes of subgroups; only the 110 normal subgroups are shown.
This group has 641 conjugacy classes of subgroups — too many to draw. Only its 110 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. C22×C4⋊AGL(1,ℤ/9) | C2 | semidirect |
| 2. 3−1+2×#121 | C2 | semidirect |
| 3. C2×#3673⋊C3 | C2 | semidirect |
| 4. #63389⋊C3 | C2 | semidirect |
| 5. #63369⋊C3 | C2 | semidirect |
| 7. #10588719 | C3 | semidirect |
| 10. C2×D4×3−1+2 | C22 | semidirect |
| 15. C4⋊C4×3−1+2 | C22 | semidirect |
| 18. C2×3−1+2⋊C8 | C22 | semidirect |
| 22. C22×D36 | C2×C3 | semidirect |
| 26. C9×#121 | C2×C3 | semidirect |
| 27. C2×#3673 | C2×C3 | semidirect |
| 28. #63389 | C2×C3 | semidirect |
| 29. #63369 | C2×C3 | semidirect |
| 44. C4⋊AGL(1,ℤ/9) | D4 | semidirect |
| 63. C2×D4×C9 | C22×C3 | semidirect |
| 70. C9×C4⋊C4 | C22×C3 | semidirect |
| 74. C2×C9⋊C8 | C22×C3 | semidirect |
| 80. C22×3−1+2 | D8 | semidirect |
| 137. D36 | C3×D4 | semidirect |
| 194. C22×C9 | C3×D8 | semidirect |
| 208. #121 | AGL(1,ℤ/9) | semidirect |
| 211. 3−1+2 | #447 | semidirect |
| 266. C2×D4 | C2×AGL(1,ℤ/9) | semidirect |
| 270. C4⋊C4 | C2×AGL(1,ℤ/9) | semidirect |
| 302. C9 | C3×#447 | semidirect |
| 340. C22 | #3673⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4⋊AGL(1,ℤ/9) | 2 |
| 3−1+2×#121 | 2 |
| C2×#3673⋊C3 | 2 |
| #63389⋊C3 | 2 |
| #63369⋊C3 | 2 |
| C3×#5036 | 3 |
| #10588719 | 3 |