Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
981 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 981 conjugacy classes of subgroups — too many to draw. Only its 96 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⋊#1084 | C2 | semidirect |
| 3. C3×Dic3×H(3,𝔽3) | C2 | semidirect |
| 6. Dic3×#272 | C3 | direct (N × H) |
| 8. C32×#272 | C4 | semidirect |
| 11. C33×Dic3 | D3 | semidirect |
| 16. C3⋊#1084 | C2×C3 | semidirect |
| 20. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 21. C32×H(3,𝔽3) | C2×C4 | semidirect |
| 36. C3×#272 | Dic3 | direct (N × H) |
| 37. C3×#272 | C3×C4 | semidirect |
| 52. C32×Dic3 | C3×D3 | semidirect |
| 59. C34 | C4×D3 | semidirect |
| 64. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 65. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 92. #272 | C3×Dic3 | direct (N × H) |
| 117. C3×Dic3 | #272 | direct (N × H) |
| 125. C33 | D3×Dic3 | semidirect |
| 126. C33 | C3×C4×D3 | semidirect |
| 132. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 179. Dic3 | C3×#272 | direct (N × H) |
| 193. C32 | C4×#272 | semidirect |
| 194. C32 | C3×D3×Dic3 | semidirect |
| 222. C3 | Dic3×#272 | direct (N × H) |
| 223. C3 | C3×C4×#272 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C32×#272 | 2 |
| C3×C3⋊#1084 | 2 |
| C3×Dic3×H(3,𝔽3) | 2 |
| C32×D3×Dic3 | 3 |
| C3×C4×#272 | 3 |
| Dic3×#272 | 3 |