Finite Group DatabasebetaFinite Group Databasebeta← C2×SL(2,𝔽3)×C3⋊Dic3 #13173175
Order 1728.
816 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 173 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 | direct (N × H) |
| 3. C2×Q8×C3⋊Dic3 | C3 | semidirect |
| 6. C2×C32×SL(2,𝔽3) | C4 | semidirect |
| 12. Q8×C3⋊Dic3 | C2×C3 | semidirect |
| 19. C32×SL(2,𝔽3) | C2×C4 | semidirect |
| 24. C2×C32×Q8 | C3×C4 | semidirect |
| 32. C2×C3×SL(2,𝔽3) | Dic3 | semidirect |
| 57. C32×Q8 | C2×C3×C4 | semidirect |
| 64. C2×C3⋊Dic3 | SL(2,𝔽3) | direct (N × H) |
| 69. C3×SL(2,𝔽3) | C2×Dic3 | semidirect |
| 77. C2×C3×Q8 | C3×Dic3 | semidirect |
| 85. C2×SL(2,𝔽3) | C3⋊Dic3 | direct (N × H) |
| 107. C3⋊Dic3 | C2×SL(2,𝔽3) | direct (N × H) |
| 121. C3×Q8 | C2×C3×Dic3 | semidirect |
| 133. SL(2,𝔽3) | C2×C3⋊Dic3 | direct (N × H) |
| 142. C2×C32 | C4×SL(2,𝔽3) | semidirect |
| 148. C2×Q8 | C3×C3⋊Dic3 | semidirect |
| 177. C32 | C2×C4×SL(2,𝔽3) | semidirect |
| 182. Q8 | C2×C3×C3⋊Dic3 | semidirect |
| 199. C2×C3 | Dic3×SL(2,𝔽3) | semidirect |
| 214. C3 | C2×Dic3×SL(2,𝔽3) | semidirect |
| 215. C2 | SL(2,𝔽3)×C3⋊Dic3 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×SL(2,𝔽3) | 2 |
| SL(2,𝔽3)×C3⋊Dic3 | 2 |
| C2×Q8×C3⋊Dic3 | 3 |
| C2×Dic3×SL(2,𝔽3) | 3 |
| C22×C3×C3⋊Dic3 | 4 |