Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
490 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 490 conjugacy classes of subgroups — too many to draw. Only its 127 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. C3×C9×C22⋊C8 | C2 | semidirect |
| 3. #11720571 | C2 | semidirect |
| 17. C9×C22⋊C8 | D3 | semidirect |
| 24. C22×C3⋊D9 | C8 | semidirect |
| 63. C3×C22⋊C8 | D9 | semidirect |
| 142. C22⋊C8 | C3⋊D9 | semidirect |
| 143. C3×C9 | #323 | semidirect |
| 216. C9 | #4468 | semidirect |
| 255. C3 | #10588146 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#88536 | 2 |
| C3×C9×C22⋊C8 | 2 |
| #11720571 | 2 |
| #10589334 | 3 |
| #10588146 | 3 |