Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
452 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 452 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.
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C22×C3 | #4185 |
| commutator, hypocenter | #732 | C2×C3×C4 |
| Frattini | C2×C32 | C2×C3×C3⋊D3 |
| Fitting, prime radical | C22×C3×#732 | C2 |
| socle | C22×C32 | #272 |
| cosocle | C2×#732 | C22×C3 |
| LCS | G ▷ #732 | |
| UCS | C1 ◁ C22×C3 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C3×#66332 | C2 | direct (N × H) |
| 5. C2×#66332 | C3 | direct (N × H) |
| 6. C2×C3×#732 | C4 | semidirect |
| 15. #66332 | C2×C3 | direct (N × H) |
| 16. C3×#732 | C2×C4 | semidirect |
| 24. C2×C3×H(3,𝔽3) | Dic3 | semidirect |
| 26. C2×C32×C9 | Dic3 | semidirect |
| 32. C2×#732 | C3×C4 | semidirect |
| 50. C3×H(3,𝔽3) | C2×Dic3 | semidirect |
| 51. C32×C9 | C2×Dic3 | semidirect |
| 54. #732 | C2×C3×C4 | semidirect |
| 70. C2×H(3,𝔽3) | C3×Dic3 | semidirect |
| 78. C2×C3×C9 | C3×Dic3 | semidirect |
| 102. H(3,𝔽3) | C2×C3×Dic3 | semidirect |
| 106. C3×C9 | C2×C3×Dic3 | semidirect |
| 168. C2×C3 | #66332 | direct (N × H) |
| 179. C3 | C2×#66332 | direct (N × H) |
| 181. C2 | C3×#66332 | 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 |
| C3×#66332 | 2 |
| C2×C3×(C3⋊Dic3)⋊C3 | 3 |
| C2×C32×Dic9 | 3 |
| C2×#66332 | 3 |