Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
276 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 276 conjugacy classes of subgroups — too many to draw. Only its 43 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⋊#63422 | C2 | semidirect |
| 3. C3×#63422 | C2 | semidirect |
| 7. D3×Q8⋊C9 | C4 | semidirect |
| 8. C3⋊(#41⋊C9) | C4 | semidirect |
| 20. #63422 | D3 | semidirect |
| 268. C3 | #10589525 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D3×#41⋊C9 | 2 |
| C3⋊#63422 | 2 |
| C3×#63422 | 2 |
| #10591670 | 3 |
| #10589525 | 3 |
| #88420 | 4 |