Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
558 conjugacy classes of subgroups; only the 102 normal subgroups are shown.
This group has 558 conjugacy classes of subgroups — too many to draw. Only its 102 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. C3×C9×#123 | C2 | semidirect |
| 3. C3×#63491 | C2 | semidirect |
| 4. C3×#63393 | C2 | semidirect |
| 5. C3×#63365 | C2 | semidirect |
| 7. #10588733 | C3 | direct (N × H) |
| 9. C22×C3×C4×C9 | C22 | semidirect |
| 17. C3×C9×C22⋊C4 | C22 | semidirect |
| 18. C3×#3676 | C22 | semidirect |
| 28. C9×#123 | C2×C3 | semidirect |
| 29. #63491 | C2×C3 | semidirect |
| 30. #63393 | C2×C3 | semidirect |
| 31. #63365 | C2×C3 | semidirect |
| 68. C22×C4×C9 | C22×C3 | semidirect |
| 79. C9×C22⋊C4 | C22×C3 | semidirect |
| 80. #3676 | C22×C3 | semidirect |
| 100. C3×#123 | D9 | semidirect |
| 165. C22×C3×C4 | C2×D9 | semidirect |
| 182. C3×C22⋊C4 | C2×D9 | semidirect |
| 223. #123 | C3×D9 | semidirect |
| 226. C3×C9 | #458 | semidirect |
| 290. C22×C4 | C2×C3×D9 | semidirect |
| 296. C22⋊C4 | C2×C3×D9 | semidirect |
| 333. C9 | C3×#458 | semidirect |
| 380. C3 | #10588733 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#63710 | 2 |
| C3×C9×#123 | 2 |
| C3×#63491 | 2 |
| C3×#63393 | 2 |
| C3×#63365 | 2 |
| C3×#5053 | 3 |
| #10588733 | 3 |