Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
502 conjugacy classes of subgroups; only the 71 normal subgroups are shown.
This group has 502 conjugacy classes of subgroups — too many to draw. Only its 71 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. C2×C9×C22⋊A4 | C2 | semidirect |
| 2. C9×#120⋊C3 | C2 | direct (N × H) |
| 4. C2×C9×#120 | C3 | semidirect |
| 5. C2×#120⋊C9 | C3 | semidirect |
| 6. C9×C22⋊A4 | C22 | semidirect |
| 9. C25×C9 | C2×C3 | semidirect |
| 10. C2×C22⋊(C22⋊C9) | C2×C3 | semidirect |
| 14. C9×#120 | C2×C3 | semidirect |
| 16. #120⋊C9 | C2×C3 | semidirect |
| 21. C2×#120⋊C3 | C9 | direct (N × H) |
| 28. C24×C9 | A4 | semidirect |
| 29. C24×C9 | C22×C3 | semidirect |
| 30. C22⋊(C22⋊C9) | C22×C3 | semidirect |
| 43. C2×C22⋊A4 | C2×C9 | semidirect |
| 48. #120⋊C3 | C2×C9 | direct (N × H) |
| 69. C23×C9 | C2×A4 | semidirect |
| 78. C2×#120 | C3×C9 | semidirect |
| 87. C22⋊A4 | C22×C9 | semidirect |
| 121. C25 | C2×C3×C9 | semidirect |
| 124. #120 | C2×C3×C9 | semidirect |
| 162. C2×C9 | #120⋊C3 | direct (N × H) |
| 167. C24 | C9×A4 | semidirect |
| 168. C24 | C22×C3×C9 | semidirect |
| 200. C9 | C2×#120⋊C3 | direct (N × H) |
| 218. C23 | C2×C9×A4 | semidirect |
| 258. C2 | C9×#120⋊C3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9×C22⋊A4 | 2 |
| C9×#120⋊C3 | 2 |
| C2×C3×#120⋊C3 | 3 |
| C2×C9×#120 | 3 |
| C2×#120⋊C9 | 3 |
| C22×C9×A4 | 4 |