Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
132 conjugacy classes of subgroups; only the 36 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 36 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 |
|---|---|---|
| 3. C9×#383 | C3 | semidirect |
| 4. #383⋊C9 | C3 | semidirect |
| 6. C9⋊(C42⋊C3) | C4 | semidirect |
| 22. C42×C9 | C3×C4 | semidirect |
| 23. C42⋊C9 | C3×C4 | semidirect |
| 40. #383 | 3−1+2 | semidirect |
| 82. C42 | C4×3−1+2 | semidirect |
| 94. C9 | #383⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C9⋊(C42⋊C3) | 2 |
| C3×#383⋊C3 | 3 |
| C9×#383 | 3 |
| #383⋊C9 | 3 |
| C4×C9⋊A4 | 4 |