Finite Group DatabasebetaFinite Group DatabasebetaOrder 1728.
644 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 644 conjugacy classes of subgroups — too many to draw. Only its 121 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. SL(2,𝔽3)×C3⋊Dic3 | C2 | semidirect |
| 3. #41×C3⋊Dic3 | C3 | semidirect |
| 5. C32×#41⋊C3 | C4 | semidirect |
| 18. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 22. C32×#41 | C3×C4 | semidirect |
| 28. C3×#41⋊C3 | Dic3 | semidirect |
| 64. C3×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 69. C3×#41 | C3×Dic3 | semidirect |
| 75. #41⋊C3 | C3⋊Dic3 | direct (N × H) |
| 95. C3⋊Dic3 | #41⋊C3 | direct (N × H) |
| 119. SL(2,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 128. #41 | C3×C3⋊Dic3 | semidirect |
| 153. C32 | C4×#41⋊C3 | semidirect |
| 183. C3 | Dic3×#41⋊C3 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#41⋊C3 | 2 |
| SL(2,𝔽3)×C3⋊Dic3 | 2 |
| #41×C3⋊Dic3 | 3 |
| Dic3×#41⋊C3 | 3 |
| C3×C4×C3⋊Dic3 | 4 |