Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
3070 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 3070 conjugacy classes of subgroups — too many to draw. Only its 125 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 | direct (N × H) |
| 3. C26×C9 | C3 | semidirect |
| 4. C22×C22⋊(C22⋊C9) | C3 | semidirect |
| 5. C9⋊(C22⋊A4) | C22 | direct (N × H) |
| 10. C25×C9 | C2×C3 | semidirect |
| 11. C2×C22⋊(C22⋊C9) | C2×C3 | semidirect |
| 24. C24×C9 | A4 | semidirect |
| 25. C24×C9 | C22×C3 | semidirect |
| 26. C22⋊(C22⋊C9) | C22×C3 | semidirect |
| 44. C23×C9 | C2×A4 | semidirect |
| 46. C26 | 3−1+2 | semidirect |
| 69. C22×C9 | C22×A4 | semidirect |
| 70. C22×C9 | C22⋊A4 | semidirect |
| 74. C25 | C2×3−1+2 | semidirect |
| 91. C2×C9 | C2×C22⋊A4 | semidirect |
| 99. C24 | C9⋊A4 | semidirect |
| 100. C24 | C22×3−1+2 | semidirect |
| 114. C9 | C22×C22⋊A4 | semidirect |
| 124. C23 | C2×C9⋊A4 | semidirect |
| 136. C22 | C22×C9⋊A4 | semidirect |
| 137. C22 | C9⋊(C22⋊A4) | direct (N × H) |
| 142. C2 | C2×C9⋊(C22⋊A4) | 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 |
| C22×C3×C22⋊A4 | 3 |
| C26×C9 | 3 |
| C22×C22⋊(C22⋊C9) | 3 |
| C22×C9⋊A4 | 4 |