Finite Group DatabasebetaFinite Group Databasebeta← C2×C3⋊(C3⋊GU(2,𝔽3)) #13173072
Order 1728.
790 conjugacy classes of subgroups; only the 191 normal subgroups are shown.
This group has 790 conjugacy classes of subgroups — too many to draw. Only its 191 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 | direct (N × H) |
| 5. C32×#41⋊C3 | C4 | semidirect |
| 7. C2×C32×SL(2,𝔽3) | C4 | semidirect |
| 17. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 29. C3×#41⋊C3 | Dic3 | semidirect |
| 31. C2×C3×SL(2,𝔽3) | Dic3 | semidirect |
| 63. C3×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 77. #41⋊C3 | C3⋊Dic3 | semidirect |
| 79. C2×SL(2,𝔽3) | C3⋊Dic3 | semidirect |
| 119. SL(2,𝔽3) | C2×C3⋊Dic3 | semidirect |
| 126. C2×C32 | GU(2,𝔽3) | semidirect |
| 154. C32 | C2×GU(2,𝔽3) | semidirect |
| 174. C2×C3 | C3⋊GU(2,𝔽3) | semidirect |
| 186. C3 | C2×C3⋊GU(2,𝔽3) | semidirect |
| 189. C2 | C3⋊(C3⋊GU(2,𝔽3)) | 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 |
| C2×C3⋊GU(2,𝔽3) | 3 |
| C2×#63664 | 3 |
| C2×C3⋊(C3⋊(C3⋊C8)) | 4 |