Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
330 conjugacy classes of subgroups; only the 183 normal subgroups are shown.
This group has 330 conjugacy classes of subgroups — too many to draw. Only its 183 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. C2×C3⋊(C9⋊C16) | C2 | semidirect |
| 35. C22×C3×C9 | C16 | semidirect |
| 82. C22×C9 | C3⋊C16 | semidirect |
| 89. C3×C9 | C22⋊C16 | semidirect |
| 121. C22×C3 | C9⋊C16 | semidirect |
| 132. C9 | #4549 | semidirect |
| 150. C22 | C3⋊(C9⋊C16) | semidirect |
| 155. C3 | #10588226 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×C8×C9 | 2 |
| C2×C3⋊(C9⋊C16) | 2 |
| #10589415 | 3 |
| #10588226 | 3 |