Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
310 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 47 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 | direct (N × H) |
| 22. C3×Q8⋊C9 | C2×C4 | semidirect |
| 84. Q8⋊C9 | C4×D3 | semidirect |
| 260. D3 | #63422 | direct (N × H) |
| 272. C3 | C2×#63422 | 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 |
| D3×#837 | 3 |
| C2×#63422 | 3 |
| D3×C9⋊C8 | 4 |