Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
335 conjugacy classes of subgroups; only the 68 normal subgroups are shown.
This group has 335 conjugacy classes of subgroups — too many to draw. Only its 68 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 | direct (N × H) |
| 4. C2×#63422 | C3 | direct (N × H) |
| 5. C3×#41⋊C9 | C4 | semidirect |
| 7. C2×C3×Q8⋊C9 | C4 | semidirect |
| 16. #63422 | C2×C3 | direct (N × H) |
| 18. C3×Q8⋊C9 | C2×C4 | semidirect |
| 37. #41⋊C9 | C3×C4 | semidirect |
| 40. C2×Q8⋊C9 | C3×C4 | semidirect |
| 74. Q8⋊C9 | C2×C3×C4 | semidirect |
| 248. C2×C3 | #63422 | direct (N × H) |
| 262. C3 | C2×#63422 | direct (N × H) |
| 266. C2 | C3×#63422 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×#41⋊C9 | 2 |
| C3×#63422 | 2 |
| C2×C3×#837 | 3 |
| C2×#63422 | 3 |
| C2×C3×C9⋊C8 | 4 |