Finite Group DatabasebetaFinite Group DatabasebetaOrder 1944.
1182 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 1182 conjugacy classes of subgroups — too many to draw. Only its 181 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, cosocle, hypocenter | C3×#732 | C23 |
| Frattini | C32 | C22×C3⋊(C3⋊D3) |
| Fitting | C22×C3×#732 | C2 |
| socle | C22×C32 | #272 |
| LCS | G ▷ C3×#732 | |
| UCS | C1 ◁ C22 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C3×#732 | C2 | semidirect |
| 2. C2×C3⋊#4185 | C2 | direct (N × H) |
| 6. C2×C3×#732 | C22 | semidirect |
| 7. C3⋊#4185 | C22 | direct (N × H) |
| 8. C22×C3×H(3,𝔽3) | D3 | semidirect |
| 9. C22×C32×C9 | D3 | semidirect |
| 12. C22×#732 | D3 | semidirect |
| 14. C3×#732 | C23 | semidirect |
| 20. C2×C3×H(3,𝔽3) | C2×D3 | semidirect |
| 21. C2×C32×C9 | C2×D3 | semidirect |
| 24. C2×#732 | C2×D3 | semidirect |
| 31. C22×H(3,𝔽3) | C3⋊D3 | semidirect |
| 34. C22×C3×C9 | C3⋊D3 | semidirect |
| 38. C3×H(3,𝔽3) | C22×D3 | semidirect |
| 39. C32×C9 | C22×D3 | semidirect |
| 40. #732 | C22×D3 | semidirect |
| 52. C2×H(3,𝔽3) | C2×C3⋊D3 | semidirect |
| 55. C2×C3×C9 | C2×C3⋊D3 | semidirect |
| 75. H(3,𝔽3) | C22×C3⋊D3 | semidirect |
| 78. C3×C9 | C22×C3⋊D3 | semidirect |
| 100. C22×C3 | #4185 | semidirect |
| 117. C2×C3 | C2×#4185 | semidirect |
| 123. C22 | C3⋊#4185 | direct (N × H) |
| 127. C3 | C22×#4185 | semidirect |
| 130. C2 | C2×C3⋊#4185 | 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 |
| C2×C3⋊#4185 | 2 |
| C22×C3⋊((C3⋊D3)⋊C3) | 3 |
| C22×C3×C3⋊D9 | 3 |
| C22×#4185 | 3 |