Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
386 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 386 conjugacy classes of subgroups — too many to draw. Only its 104 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. Dic3×#732 | C2 | direct (N × H) |
| 3. C2×Dic3×H(3,𝔽3) | C3 | semidirect |
| 4. C2×C3×C9×Dic3 | C3 | semidirect |
| 6. C2×C3×#732 | C4 | semidirect |
| 10. Dic3×H(3,𝔽3) | C2×C3 | semidirect |
| 11. C3×C9×Dic3 | C2×C3 | semidirect |
| 16. C3×#732 | C2×C4 | semidirect |
| 22. C2×C3×H(3,𝔽3) | C3×C4 | semidirect |
| 24. C2×C32×C9 | C3×C4 | semidirect |
| 30. C2×#732 | Dic3 | direct (N × H) |
| 46. C3×H(3,𝔽3) | C2×C3×C4 | semidirect |
| 47. C32×C9 | C2×C3×C4 | semidirect |
| 50. #732 | C2×Dic3 | direct (N × H) |
| 65. C2×H(3,𝔽3) | C3×Dic3 | semidirect |
| 73. C2×C3×C9 | C3×Dic3 | semidirect |
| 96. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 100. C3×C9 | C2×C3×Dic3 | semidirect |
| 104. C2×Dic3 | #732 | direct (N × H) |
| 137. Dic3 | C2×#732 | direct (N × H) |
| 160. C2×C3 | C4×#732 | semidirect |
| 171. C3 | C2×C4×#732 | semidirect |
| 173. C2 | Dic3×#732 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C3×#732 | 2 |
| Dic3×#732 | 2 |
| C2×Dic3×H(3,𝔽3) | 3 |
| C2×C3×C9×Dic3 | 3 |
| C2×C4×#732 | 3 |