Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
464 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 464 conjugacy classes of subgroups — too many to draw. Only its 56 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. #11721330 | 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 |
| 28. C24×C9 | A4 | semidirect |
| 29. C24×C9 | C22×C3 | semidirect |
| 30. C22⋊(C22⋊C9) | C22×C3 | semidirect |
| 69. C23×C9 | C2×A4 | semidirect |
| 78. C2×#120 | 3−1+2 | semidirect |
| 121. C25 | C2×3−1+2 | semidirect |
| 124. #120 | C2×3−1+2 | semidirect |
| 162. C2×C9 | #120⋊C3 | semidirect |
| 167. C24 | C9⋊A4 | semidirect |
| 168. C24 | C22×3−1+2 | semidirect |
| 200. C9 | C2×#120⋊C3 | semidirect |
| 218. C23 | C2×C9⋊A4 | semidirect |
| 258. C2 | #11721330 | 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 |
| #11721330 | 2 |
| C2×C3×#120⋊C3 | 3 |
| C2×C9×#120 | 3 |
| C2×#120⋊C9 | 3 |
| C22×C9⋊A4 | 4 |