Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
487 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 487 conjugacy classes of subgroups — too many to draw. Only its 90 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×C3⋊GU(2,𝔽3) | C2 | semidirect |
| 3. #10593657 | C3 | direct (N × H) |
| 6. C32×#41⋊C3 | C4 | semidirect |
| 8. C2×C32×SL(2,𝔽3) | C4 | semidirect |
| 17. C3⋊GU(2,𝔽3) | C2×C3 | semidirect |
| 38. C3×#41⋊C3 | Dic3 | semidirect |
| 39. C3×#41⋊C3 | C3×C4 | semidirect |
| 44. C2×C3×SL(2,𝔽3) | Dic3 | semidirect |
| 45. C2×C3×SL(2,𝔽3) | C3×C4 | semidirect |
| 121. #41⋊C3 | C3×Dic3 | semidirect |
| 124. C2×SL(2,𝔽3) | C3×Dic3 | semidirect |
| 271. C32 | #5423 | semidirect |
| 314. C3 | C3×#5423 | semidirect |
| 315. C3 | #10593657 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41⋊C3 | 2 |
| C3×C3⋊GU(2,𝔽3) | 2 |
| #10593657 | 3 |
| C3×#5423 | 3 |
| C3×#5236 | 3 |
| C3×#3748 | 4 |